#precalculus | Mathematics | Page 117

hexed ermine Mar 27, 2018, 4:52 AM

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because there are two points where sin is -sqrt3/2

void patio Mar 27, 2018, 4:52 AM

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@upper smelt it sounds like to me you don't know the unit circle very well

hexed ermine Mar 27, 2018, 4:52 AM

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Yes

void patio Mar 27, 2018, 4:52 AM

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yeah

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oh ouch

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i understand

charred jasper Mar 28, 2018, 9:43 PM

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<@&286206848099549185> Can i get some help on parametric equations?

charred jasper Mar 28, 2018, 9:58 PM

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please

gritty blaze Mar 28, 2018, 10:02 PM

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Show it !!!

true vigil Mar 28, 2018, 10:32 PM

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yeah just ask!

thick raptor Mar 29, 2018, 2:20 AM

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rip

prisma tapir Apr 1, 2018, 3:11 AM

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not sure of this would be in calc or precalc but does anyone know how to help me with this
i know that the sum from k=0 to n of k^2 = (n(n+1)(2n+1))/6
but how would you do it for any power like 5 or 1/2

gleaming wing Apr 1, 2018, 7:31 AM

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Math steps unclear. Now stuck in the 5th dimension. What do?

zenith juniper Apr 1, 2018, 3:30 PM

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Hi. Where can I find hard questions that are tricky and so regarding a certain subject?

granite stirrupBOT Apr 1, 2018, 5:40 PM

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📎 latex.png

viscid thistle Apr 2, 2018, 12:33 AM

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what ^

viscid thistle Apr 2, 2018, 2:57 AM

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Can someone help me with this? I am not sure how to follow

📎 unknownPer.png

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📎 unknown.png

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I got -1 for Horizontal asymptote, and -2 & 2 for vertical asymptote but it

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'is incorrect

clever inlet Apr 2, 2018, 3:02 AM

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how'd you get -1 for horizontal asymptote?

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@viscid thistle

viscid thistle Apr 2, 2018, 3:13 AM

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where the top part intercepts athe the infinite curve

clever inlet Apr 2, 2018, 3:13 AM

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?

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just use the red dotted horizontal line

viscid thistle Apr 2, 2018, 3:14 AM

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I thought that was the y-intercept asymptote

clever inlet Apr 2, 2018, 3:15 AM

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?

hexed ermine Apr 2, 2018, 5:52 AM

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Lol

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The y-intercept asymptote

clever inlet Apr 2, 2018, 7:05 AM

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Don't all horizontal asymptotes have some form of y intercept?

hexed ermine Apr 2, 2018, 7:28 AM

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Indeed so

true vigil Apr 2, 2018, 7:28 AM

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thonker

odd lichen Apr 2, 2018, 8:08 AM

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@clever inlet you still need help?

queen ibex Apr 2, 2018, 5:52 PM

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Can someone help me with this question pls??

📎 JPEG_20180402_105157.jpg

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Dont mind the math test mark lol

viscid thistle Apr 2, 2018, 5:53 PM

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7?

queen ibex Apr 2, 2018, 5:53 PM

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yep

hexed ermine Apr 2, 2018, 6:03 PM

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Okay

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So you started off a bit correct

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You want to determine the amplitude and and the vertical shift

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which so far would be 4cos(x)-1

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now what we need is the b and c value

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@queen ibex

queen ibex Apr 2, 2018, 6:06 PM

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ok how do i find that? thats where im lost on

hexed ermine Apr 2, 2018, 6:06 PM

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Alright

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so first find the period

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What you want to do is subtract the x coordinates

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$$\frac{\pi}{6}-\frac{-\pi}{3}$$

granite stirrupBOT Apr 2, 2018, 6:07 PM

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📎 latex.png

hexed ermine Apr 2, 2018, 6:07 PM

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Using simple algebra

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pi/6-(-2pi/6)=pi/2

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Got it so far?

queen ibex Apr 2, 2018, 6:08 PM

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yea

hexed ermine Apr 2, 2018, 6:08 PM

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Okay so that's the distance from the minimum to the maximum

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that means its a half a period

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so multiply that by 2 to get the full period

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Which is just pi

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so pi is the period

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Now you know that 2pi/b is the period right?

queen ibex Apr 2, 2018, 6:09 PM

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yep

hexed ermine Apr 2, 2018, 6:09 PM

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Okay so we do 2pi/b=pi

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since pi is the period

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and we can say that b is 2

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2pi/2 = pu

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pi*

queen ibex Apr 2, 2018, 6:10 PM

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Wait dont u do 2pi/b=7pi/6?

hexed ermine Apr 2, 2018, 6:10 PM

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No

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pi is the period

queen ibex Apr 2, 2018, 6:11 PM

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ok

hexed ermine Apr 2, 2018, 6:11 PM

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Okay so we have so far

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4cos(2x)-1

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now lastly we need to find the phase shift

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Which is defined as c/b

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Now I prefer to use cosine first bc it's easier for this problem imo

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I notice that the maximum is pi/6 to the right

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So what I can do is c/b=pi/6

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and we said that b is 2 already

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$$\frac{c}{2}=\frac{\pi}{6}$$

granite stirrupBOT Apr 2, 2018, 6:13 PM

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📎 latex.png

hexed ermine Apr 2, 2018, 6:13 PM

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Cross multiply 2pi=6c

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c=pi/3

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There you have it

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and since it's pi/6 to the right you do -pi/6

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So we have as a final answer..

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$$4\cos(2x-\frac{\pi}{3})-1$$

granite stirrupBOT Apr 2, 2018, 6:15 PM

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📎 latex.png

hexed ermine Apr 2, 2018, 6:15 PM

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got it?

queen ibex Apr 2, 2018, 6:15 PM

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yep

hexed ermine Apr 2, 2018, 6:16 PM

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Alright and finding the sin is answer

queen ibex Apr 2, 2018, 6:16 PM

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i didnt know u can find the shift like that

hexed ermine Apr 2, 2018, 6:16 PM

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You can!

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So do you know how to find sin version?

queen ibex Apr 2, 2018, 6:16 PM

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is it the same thing but different shift value??

hexed ermine Apr 2, 2018, 6:16 PM

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yep!

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pi/2 degrees out of shift

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so just add pi/2

queen ibex Apr 2, 2018, 6:17 PM

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ok thank you so much

hexed ermine Apr 2, 2018, 6:17 PM

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No problem

queen ibex Apr 2, 2018, 7:03 PM

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@hexed ermine can C/B to find phase shift can be used for sine equations as well???

hexed ermine Apr 2, 2018, 7:03 PM

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Indeed

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the only thing you need to do is add pi/2

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since cosine and sine waves are 90 degrees out of sync

queen ibex Apr 2, 2018, 7:13 PM

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ok thank you

fringe stream Apr 3, 2018, 4:31 AM

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https://puu.sh/zVaIz/460a9558f0.png

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I highlighted the important parts for you

viscid thistle Apr 3, 2018, 6:39 AM

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Draw a force body diagram first @upper smelt

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So just draw a diagram first showing the respective forces

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Yes

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Weird that forces are in kg not N

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Oh I see

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Anyways, you could decompose each vector into their x and y components then add them up for resultant force

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Assume one of the forces is parallel to the x axis for convenience

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How does your pic look like, I'm on android so can't draw sorry

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If you draw a diagram, the x component is just cos theta multiplied by the magnitude of the vector

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Y is sin theta nultiplied by mag

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Add together the components, use pythag to find magnitude: sqrt (x^2 + y^2)

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Angle is just arctan y/x

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Nice, there's an answer on homework help server too for your q @upper smelt

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Same method

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Llama's method is probably best way

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That's what I would've done

severe snow Apr 3, 2018, 7:57 AM

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can anyone help me with parametric equations

viscid thistle Apr 3, 2018, 7:59 AM

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Ok

severe snow Apr 3, 2018, 8:04 AM

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@viscid thistle How do I graph this stuff

viscid thistle Apr 3, 2018, 8:05 AM

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What are the eqns

severe snow Apr 3, 2018, 8:06 AM

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x=4cos^3(t)

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y=2sin^3(t)

viscid thistle Apr 3, 2018, 8:07 AM

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Add them

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x+y=4cos3 (t)+2sin3 (t)

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Try get rid of the t

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Then you are left with only x and y then you can graph

fringe stream Apr 3, 2018, 4:30 PM

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@cosmic nacelle

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=tex \sin ^2 (x) \leq \dfrac{1}{2} ~in~ 0\leq x <2\pi

granite stirrupBOT Apr 3, 2018, 4:30 PM

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📎 latex.png

cosmic nacelle Apr 3, 2018, 4:31 PM

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yeah

fringe stream Apr 3, 2018, 4:32 PM

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What have you tried?

cosmic nacelle Apr 3, 2018, 4:33 PM

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ive already tried 0<=x<=pi/4, 3pi/4<2pi

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@fringe stream hello?

fringe stream Apr 3, 2018, 4:41 PM

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Oh sorry

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$$-\frac1{\sqrt2} \leq \sin{x} \leq \frac1{\sqrt2}$$

granite stirrupBOT Apr 3, 2018, 4:41 PM

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📎 latex.png

fringe stream Apr 3, 2018, 4:41 PM

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Try solving this

cosmic nacelle Apr 3, 2018, 4:42 PM

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umm

fringe stream Apr 3, 2018, 4:43 PM

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=pup sinx from 0 to 2pi

granite stirrupBOT Apr 3, 2018, 4:43 PM

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📎 result.png

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Query made by @fringe stream
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=sinx+from+0+to+2pi
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/

cosmic nacelle Apr 3, 2018, 4:43 PM

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0<=x<=pi/4

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3pi<=x<=5pi/4

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7pi<=x<2pi

fringe stream Apr 3, 2018, 4:45 PM

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All values of x greater than that for which sin(x) is -1/sqrt2, and all values of x less than that for which sin(x) is 1/sqrt2

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Between 0 to 2pi

cosmic nacelle Apr 3, 2018, 4:46 PM

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???

fringe stream Apr 3, 2018, 4:47 PM

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=pup solve -1/sqrt(2) <= sin(x) <= 1/sqrt(2)

granite stirrupBOT Apr 3, 2018, 4:47 PM

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📎 result.png

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Query made by @fringe stream
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=solve+-1%2Fsqrt(2)+<%3D+sin(x)+<%3D+1%2Fsqrt(2)
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/

fringe stream Apr 3, 2018, 4:47 PM

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=pup solve -1/sqrt(2) <= sin(x) <= 1/sqrt(2), x between 0 and 2pi

granite stirrupBOT Apr 3, 2018, 4:47 PM

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📎 result.png

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Query made by @fringe stream
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=solve+-1%2Fsqrt(2)+<%3D+sin(x)+<%3D+1%2Fsqrt(2)%2C+x+between+0+and+2pi
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/

fringe stream Apr 3, 2018, 4:48 PM

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=pup solve -1/sqrt(2) <= sin(x) <= 1/sqrt(2), 0 <= x < 2pi

granite stirrupBOT Apr 3, 2018, 4:48 PM

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📎 result.png

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Query made by @fringe stream
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=solve+-1%2Fsqrt(2)+<%3D+sin(x)+<%3D+1%2Fsqrt(2)%2C+0+<%3D+x+<+2pi
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/

cosmic nacelle Apr 4, 2018, 3:30 AM

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hey @fringe stream i put in your answer, and it was wrong

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idk why

dense zealot Apr 4, 2018, 5:13 AM

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Lol

simple vault Apr 6, 2018, 4:15 AM

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📎 unknown.png

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#8

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I dont understand how to do those kind of questions

hexed ermine Apr 6, 2018, 4:28 AM

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Make time stamps and plot it on a graph

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If it makes 1.5revolutions per minute/ that means it makes 1 revolution every 1/1.5minutes

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so 1 revolution = 40sec

hexed ermine Apr 6, 2018, 4:46 AM

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You know i've been working through this problem and im not sure if you can do it

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📎 Screenshot_14.png

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This is the closest thing I have to it

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you need a function where it goes up and down in a linear fashion and im not sure if there is a way

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<@&286206848099549185>

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Maybe they might know

grizzled hull Apr 6, 2018, 4:52 AM

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Gut says $$150\sin\left(1.5x\right)+156$$

granite stirrupBOT Apr 6, 2018, 4:52 AM

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📎 latex.png

grizzled hull Apr 6, 2018, 4:52 AM

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No, no....

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$$-75\cos(\frac{3}{4\pi}x)+75+6$$

granite stirrupBOT Apr 6, 2018, 4:55 AM

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📎 latex.png

simple vault Apr 6, 2018, 4:56 AM

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I dont understand how you got that @grizzled hull

grizzled hull Apr 6, 2018, 4:56 AM

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I'm still editing it.

simple vault Apr 6, 2018, 4:56 AM

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ok

hexed ermine Apr 6, 2018, 4:56 AM

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I mean I think mine would be correct maybe thonker

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$$|150\sin(\frac{\pi}{40}x)|+6$$

granite stirrupBOT Apr 6, 2018, 4:59 AM

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📎 latex.png

hexed ermine Apr 6, 2018, 4:59 AM

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Final answer lol

simple vault Apr 6, 2018, 4:59 AM

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it doesnt say its right on the website

hexed ermine Apr 6, 2018, 4:59 AM

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huh okay I guess ill wait for Shenzao

simple vault Apr 6, 2018, 4:59 AM

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I hate webassign lol

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wouldnt the amplitude be 156?

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since its 150 feet + the wheel(6)

grizzled hull Apr 6, 2018, 5:01 AM

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Want amplitude to be radius.

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Radius is 75

hexed ermine Apr 6, 2018, 5:01 AM

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but mine is in seconds

grizzled hull Apr 6, 2018, 5:01 AM

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We translate it up by radius + height above ground

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So we have at least $$-75\cos(_)+81$$

granite stirrupBOT Apr 6, 2018, 5:01 AM

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📎 latex.png

grizzled hull Apr 6, 2018, 5:02 AM

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I just need to figure out how to make periodicity of -cos(x) 1.

hexed ermine Apr 6, 2018, 5:02 AM

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2pi/b=period

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1.5minute is one period

grizzled hull Apr 6, 2018, 5:03 AM

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Mm. Didn't see"minute" there.

hexed ermine Apr 6, 2018, 5:03 AM

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oops

grizzled hull Apr 6, 2018, 5:03 AM

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still, 1.5 per minute is 3 per two minutes.

hexed ermine Apr 6, 2018, 5:04 AM

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1.5revoltions per minute :v

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so 2/3 is period

simple vault Apr 6, 2018, 5:04 AM

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I get the period from the revs/min?

hexed ermine Apr 6, 2018, 5:04 AM

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It makes one revolution in 40seconds

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or 2/3 minutes

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so put 3pi as b????

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2pi/b=2/3

grizzled hull Apr 6, 2018, 5:07 AM

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$$-75\cos\left(3\pi x\right)+81$$

granite stirrupBOT Apr 6, 2018, 5:07 AM

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📎 latex.png

grizzled hull Apr 6, 2018, 5:07 AM

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I like this one.

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Feels right.

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3 full revolutions in 2 minutes.

hexed ermine Apr 6, 2018, 5:08 AM

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Yes

grizzled hull Apr 6, 2018, 5:08 AM

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Minimum height is 6.

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Maximum height is 156.

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Feels right.

hexed ermine Apr 6, 2018, 5:09 AM

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Looks correct to me

grizzled hull Apr 6, 2018, 5:09 AM

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@simple vault $$-75\cos\left(3\pi x\right)+81$$

granite stirrupBOT Apr 6, 2018, 5:09 AM

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📎 latex.png

grizzled hull Apr 6, 2018, 5:13 AM

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I dunno, I like $$-r\cos(2\pi\omega x)+r+h$$

granite stirrupBOT Apr 6, 2018, 5:13 AM

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📎 latex.png

grizzled hull Apr 6, 2018, 5:13 AM

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Let omega be the number of revolutions in a minute.

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r is the radius of the ferris wheel.

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h is the distance off the ground from the lowest point.

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the negative starts it at the bottom.

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Let it be positive if it starts at the top.

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Use sin if it starts in the middle.

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This make sense @simple vault ?

hexed ermine Apr 6, 2018, 5:15 AM

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I was on the right track :v

simple vault Apr 6, 2018, 5:23 AM

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That answer was incorrect

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from what it shows on webassign

hexed ermine Apr 6, 2018, 5:23 AM

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Lol savage

grizzled hull Apr 6, 2018, 5:23 AM

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Did we miss a small detail?

fringe stream Apr 6, 2018, 5:24 AM

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It doesn't say if t is in minutes or seconds

grizzled hull Apr 6, 2018, 5:24 AM

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wrote it in terms of h and t, yes?

fringe stream Apr 6, 2018, 5:24 AM

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Try seconds maybe

grizzled hull Apr 6, 2018, 5:25 AM

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Something friendlier to the website may be $$h=-75\cos(3\pi t)+81$$

granite stirrupBOT Apr 6, 2018, 5:25 AM

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📎 latex.png

grizzled hull Apr 6, 2018, 5:25 AM

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Since it specified that it needed to be an equation in terms of h and t.

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If you already did that, we'd just need to turn 3 into 180 to get it into seconds, I think.

fringe stream Apr 6, 2018, 5:29 AM

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Nope

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pi/20

hexed ermine Apr 6, 2018, 5:29 AM

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yep

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$$h = -75\cos(\frac{\pi}{20}t)+81$$

granite stirrupBOT Apr 6, 2018, 5:30 AM

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📎 latex.png

hexed ermine Apr 6, 2018, 5:30 AM

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Try that @simple vault

grizzled hull Apr 6, 2018, 5:31 AM

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Graphed that.

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It looks way off.

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No

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It looks perfect.

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Kill me.

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I did that right, then edited it 6 times.

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It seems I'm no longer confident.

hexed ermine Apr 6, 2018, 5:32 AM

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Nah your equation was good in terms on minutes

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They really need to specify

simple vault Apr 6, 2018, 5:35 AM

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@hexed ermine also incorrect :/

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📎 unknown.png

fringe stream Apr 6, 2018, 5:36 AM

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It says equation

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Try h = <...>?

grizzled hull Apr 6, 2018, 5:36 AM

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Where is your h=?

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It wants an equation.

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Needs an =

simple vault Apr 6, 2018, 5:45 AM

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📎 unknown.png

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um...?

fringe stream Apr 6, 2018, 5:46 AM

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Where's the h?

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Do you need it written out for you?

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Which, btw, has already been done, multiple times

hexed ermine Apr 6, 2018, 5:47 AM

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📎 Screenshot_20180406-014656.jpg

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Write it just like that

fringe stream Apr 6, 2018, 5:48 AM

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If that doesn't work, replace pi/20 with 3pi

simple vault Apr 6, 2018, 5:59 AM

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3pi worked

hexed ermine Apr 6, 2018, 6:01 AM

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:+1:

simple vault Apr 6, 2018, 8:08 AM

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so I have these set of problems here but I don't know how to go about approaching them. The textbook doesn't have good examples of it either

📎 unknown.png

clever inlet Apr 6, 2018, 8:24 AM

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Think about what inverses do

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They basically undo each other right?

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@simple vault

simple vault Apr 6, 2018, 8:25 AM

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yes

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wait

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so they cancel out?

clever inlet Apr 6, 2018, 8:25 AM

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Yes

simple vault Apr 6, 2018, 8:25 AM

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and the answer is whats left

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in the parenthesis

clever inlet Apr 6, 2018, 8:25 AM

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It's the number

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Yes

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The arcsin function does something to the number

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And then the sine function undoes that

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Giving back your original number

simple vault Apr 6, 2018, 8:26 AM

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okay now what is the inverse is outside of the parenthesis?

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if*

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if the inverse is outside and the sine/cosine/tan is inside

clever inlet Apr 6, 2018, 8:27 AM

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I mean

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They're still inverses to each other

simple vault Apr 6, 2018, 8:27 AM

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so theyd still cancel eachother out?

clever inlet Apr 6, 2018, 8:27 AM

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Yeah

stark trench Apr 7, 2018, 11:46 PM

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📎 Screenshot_20180407-161415.jpg

true vigil Apr 8, 2018, 1:44 AM

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mostly try to find the equation of the parabola

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put the coordinate system with (0,0) at the vertex

pure hazel Apr 8, 2018, 8:34 PM

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📎 26suq7.jpg

hexed ermine Apr 8, 2018, 9:35 PM

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Where is the law of tangents 🤔

mortal basin Apr 9, 2018, 1:18 AM

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what is the symmetry of sin and cos

ornate notch Apr 9, 2018, 1:19 AM

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Could you elaborate a bit more on that?

mortal basin Apr 9, 2018, 1:23 AM

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Sorry

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Im reviewing my test

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And the question is what type of symmetry does f(x)=sin(x) have?

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I said neither

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But that because i compeltely forgot

ornate notch Apr 9, 2018, 1:26 AM

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Oh, well, cos has reflective symmetry over the y axis then

hexed ermine Apr 9, 2018, 1:31 AM

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^

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And sin(x) has symmetry at pi/2+pik

mortal basin Apr 9, 2018, 1:33 AM

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But its asking for odd or even

hexed ermine Apr 9, 2018, 1:43 AM

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For sin(x) at 0; it's odd

viscid thistle Apr 9, 2018, 2:21 AM

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Could anyone help me with this?

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📎 sample_.png

dense zealot Apr 9, 2018, 2:22 AM

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Yes x(x-2)(x-4)

viscid thistle Apr 9, 2018, 2:22 AM

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For f(x)>0
I presumed that the area in between is (2,0)∩(4,0)

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but I got that wrong

viscid thistle Apr 9, 2018, 2:47 AM

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I think it's actually negative

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but you can't go below two 0's in one place

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so I am not sure how to write this

clever inlet Apr 9, 2018, 4:56 AM

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That does not look right

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Go from left to right

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It's positive from negative infinity to 0

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And again from 2 to 4

wraith shell Apr 9, 2018, 8:14 AM

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Hello, is anyone available to help me understand how future and present values work? I was trying to answer the following question : "How does the interest rate affect the present and future values of an annuity?" This is my answer but after thinking about it more I don't think it is correct : "Assuming the time it takes to pay off a loan stays the same, the present value of an annuity with higher interests rates will have to pay larger annuities while the present value of an annuity with lower interest rates will have to play smaller annuities. Assuming the time given to future value annuity and the outcome is the same, higher interest rates correlate to lower annuities and lower interest rates correlate to higher annuities." It seems the more I think about this I start to get it and then I confuse myself.

wraith shell Apr 10, 2018, 1:17 AM

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Could you answer the question "how does the interest rate affect the present and future values of an annuity?" by saying...

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Higher interest rates increase the future value, and lower interest rates increase the present value?

rotund musk Apr 10, 2018, 3:27 AM

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can someone help me simplify a trig expression?

haughty thicket Apr 10, 2018, 3:28 AM

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If you send the trig identity sheet

rotund musk Apr 10, 2018, 3:28 AM

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well I can't find a good trig identity for sin(sq)x-1

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there are a bunch for 1-sin(sq)x

wintry moat Apr 10, 2018, 3:39 AM

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https://www.symbolab.com/solver/trigonometric-simplification-calculator

Trigonometric Simplification Calculator - Symbolab

Free trigonometric simplification calculator - Simplify trigonometric expressions to their simplest form step-by-step

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here is the right one then

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naturally it should work

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got something

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@rotund musk

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just found : -1+sin(s*q)*x

rotund musk Apr 10, 2018, 3:42 AM

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that doesn't work. I just checked.

wintry moat Apr 10, 2018, 3:43 AM

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yeah checked too

rotund musk Apr 10, 2018, 3:43 AM

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wait

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yes it does

wintry moat Apr 10, 2018, 3:43 AM

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website is shitty

rotund musk Apr 10, 2018, 3:43 AM

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SHIT

wintry moat Apr 10, 2018, 3:43 AM

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oh

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lol

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http://www.webmath.com/trigsimp.html

Simplify a Trigonometric Expression - WebMath

Simplify a Trigonometric Expression - powered by WebMath

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had also this one in mind

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hope i couldve help you a bit

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😃

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first it was like ( dosent support multiple functions ) and then you just had to adjust it a bit

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I believe that the internet/ computing all these huge ressources made possible a lot of complex / boring tasks such as these calculations and made our lives just simpler and eaiser. If you were to go on math , go on computational / symbolic algebra

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machines do the hard work for you

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Like imagine a huge repertoire where hunders and thousands of devolopers contribute their efforts in calculating stuff like a huge dictionnary and compile all of that

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main intrest left is just to learn new concepts on and on

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back then it was just as boring as it might seem

viscid thistle Apr 10, 2018, 6:05 AM

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Calculatorsbare best

candid vine Apr 11, 2018, 1:24 AM

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📎 Screenshot_20180411-032428.png

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Wow.

viscid thistle Apr 11, 2018, 1:32 AM

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👌

dense zealot Apr 11, 2018, 2:18 AM

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@candid vine did u simplify it

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It's the imaginary part of (cosx + isinx)^17 divided by i

candid vine Apr 11, 2018, 2:19 AM

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I can complexify it

dense zealot Apr 11, 2018, 2:19 AM

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U can use binomial theorem

static zinc Apr 11, 2018, 12:36 PM

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Regarding my question yesterday, this is what I needed:

granite stirrupBOT Apr 11, 2018, 12:36 PM

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📎 latex.png

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📎 latex.png

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📎 latex.png

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📎 latex.png

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📎 latex.png

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📎 latex.png

static zinc Apr 11, 2018, 12:40 PM

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And from then I look up the value in radians and solve for x. Sorry for the mess

naive surge Apr 12, 2018, 6:52 PM

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do you guys have any tips on remembering reduction, half-angle, etc. formulas other than just writing it a ton.

true vigil Apr 12, 2018, 6:56 PM

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half angle formulas are dumb

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you can get all of them from sin though

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by noting cos(x) = sin(x+pi/2)

naive surge Apr 12, 2018, 6:58 PM

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lright thank you

eternal solstice Apr 12, 2018, 8:45 PM

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Ok this problem is driving me crazy.

📎 Screen_Shot_2018-04-12_at_1.44.36_PM.png

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I know that the Amp = 2 , Midline = 0 and the Period is 6 which is 2pi/6 so pi/3

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It is a cosine function shifted to the right one unit so that would be -1

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Therefore the answer should be -2cos(pi/3x - 1 )

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It looks almost identical on desmos but I cant get it to line up perfectly.

rocky bison Apr 12, 2018, 8:47 PM

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ok

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So starting with

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You want to use cos

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Now

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=pup plot cos(x)

granite stirrupBOT Apr 12, 2018, 8:47 PM

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📎 result.png

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📎 result.png

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Query made by @rocky bison
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=plot+cos(x)
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/

rocky bison Apr 12, 2018, 8:47 PM

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Now problem 1

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cos only goes between 1 and -1

eternal solstice Apr 12, 2018, 8:48 PM

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Ok

rocky bison Apr 12, 2018, 8:48 PM

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You want 2 and -2

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So you're going to just multiply by 2

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So currently we have 2cos(x)

eternal solstice Apr 12, 2018, 8:48 PM

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Amplitude should = 2

rocky bison Apr 12, 2018, 8:48 PM

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Which lines up in y

eternal solstice Apr 12, 2018, 8:48 PM

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yeah

rocky bison Apr 12, 2018, 8:48 PM

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=pup graph 2cos(x)

granite stirrupBOT Apr 12, 2018, 8:48 PM

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📎 result.png

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📎 result.png

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Query made by @rocky bison
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=graph+2cos(x)
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/

rocky bison Apr 12, 2018, 8:48 PM

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Looks good

eternal solstice Apr 12, 2018, 8:48 PM

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Yep.

rocky bison Apr 12, 2018, 8:48 PM

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Now

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Period is 6

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So we need to somehow convert our current period of 2pi

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into 6

eternal solstice Apr 12, 2018, 8:49 PM

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divide 2pi by 6 and simplify

rocky bison Apr 12, 2018, 8:49 PM

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I'm going to do this algebraically

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Just for clarity

eternal solstice Apr 12, 2018, 8:50 PM

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Sure thanks

rocky bison Apr 12, 2018, 8:50 PM

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Some multiple of 2pi will equal 6

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let's call it k

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So =tex 2k\pi=6

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=tex 2k\pi=6

granite stirrupBOT Apr 12, 2018, 8:50 PM

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📎 latex.png

rocky bison Apr 12, 2018, 8:50 PM

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Now we're just going to solve got k

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=tex k=\frac{6}{2\pi}=\frac{3}{\pi}

granite stirrupBOT Apr 12, 2018, 8:50 PM

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📎 latex.png

rocky bison Apr 12, 2018, 8:51 PM

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nice

eternal solstice Apr 12, 2018, 8:51 PM

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Oooh

rocky bison Apr 12, 2018, 8:51 PM

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btw this is using radians hopefully that's no issue

eternal solstice Apr 12, 2018, 8:51 PM

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I think that might be where I messed up?

rocky bison Apr 12, 2018, 8:51 PM

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Hold up

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We want the inverse of that function

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Because we'll be making a transformation

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Of type

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f(ax)

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Which is a "squeeze" of a

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Wait no that's good, 6 is less than pi

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nvm

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Let's graph it and see if period is correct though

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=pup plot 2\cos(\frac{3x}{\pi})

granite stirrupBOT Apr 12, 2018, 8:52 PM

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📎 result.png

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📎 result.png

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📎 result.png

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Query made by @rocky bison
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=plot+2\cos(\frac{3x}{\pi})
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/

rocky bison Apr 12, 2018, 8:53 PM

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ok

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that's a little bit off

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So there's an issue somewhere here

eternal solstice Apr 12, 2018, 8:53 PM

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I think pi/3 might be the correct period

rocky bison Apr 12, 2018, 8:53 PM

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Yep

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It is

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It is the reciprocal

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1/a

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stupid mistake

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whatever though

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=pup graph 2cos(\frac{\pi x}{3})

granite stirrupBOT Apr 12, 2018, 8:54 PM

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📎 result.png

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📎 result.png

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📎 result.png

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Query made by @rocky bison
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=graph+2cos(\frac{\pi+x}{3})
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/

rocky bison Apr 12, 2018, 8:54 PM

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ok

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perfect

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now last

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we want the first peak

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at -2

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you can choose any point on the graph

eternal solstice Apr 12, 2018, 8:54 PM

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so -A

rocky bison Apr 12, 2018, 8:54 PM

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just make it consistent

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not -a

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+a

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It's of type

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f(x+a)

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which shifts everything left

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by a

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So from 0 to 2

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2

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=pup graph 2\cos(\frac{x\pi}{3}+2)

granite stirrupBOT Apr 12, 2018, 8:55 PM

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📎 result.png

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📎 result.png

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📎 result.png

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Query made by @rocky bison
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=graph+2\cos(\frac{x\pi}{3}%2B2)
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/

rocky bison Apr 12, 2018, 8:55 PM

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Looks pretty good

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So your function

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=tex 2\cos\left(\frac{x\pi}{3}+2\right)

granite stirrupBOT Apr 12, 2018, 8:56 PM

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📎 latex.png

rocky bison Apr 12, 2018, 8:56 PM

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Hopefully that was useful to you

eternal solstice Apr 12, 2018, 8:56 PM

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It was

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But the software doesn't like that answer either.

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But it does look very similar to it on desmos

rocky bison Apr 12, 2018, 8:57 PM

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what software?

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desmos?

eternal solstice Apr 12, 2018, 8:58 PM

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myopenmath

📎 Screen_Shot_2018-04-12_at_1.57.59_PM.png

rocky bison Apr 12, 2018, 8:59 PM

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probably because it wants sin

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not cos

eternal solstice Apr 12, 2018, 9:00 PM

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Ok. So the amplitude and the period and the midline will be the same

rocky bison Apr 12, 2018, 9:00 PM

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Not sure what midline is

eternal solstice Apr 12, 2018, 9:00 PM

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So i just need to find the horizontal shift

rocky bison Apr 12, 2018, 9:00 PM

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Ye

eternal solstice Apr 12, 2018, 9:00 PM

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midline is y=0

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the line that shifts the graph directly in the middle

rocky bison Apr 12, 2018, 9:01 PM

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Urm

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well

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just use

eternal solstice Apr 12, 2018, 9:01 PM

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splits*

rocky bison Apr 12, 2018, 9:01 PM

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=tex \sin(x)=\cos\left(x-\frac{\pi}{2}\right)

granite stirrupBOT Apr 12, 2018, 9:01 PM

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📎 latex.png

rocky bison Apr 12, 2018, 9:01 PM

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Although might not like that

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Might be easier starting agian

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Also tests your understanding

eternal solstice Apr 12, 2018, 9:02 PM

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like a new problem completely?

rocky bison Apr 12, 2018, 9:02 PM

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yeah

eternal solstice Apr 12, 2018, 9:03 PM

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I can reset it. Ok

rocky bison Apr 12, 2018, 9:03 PM

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I'm heading to sleep though, so goodluck 😃

eternal solstice Apr 12, 2018, 9:03 PM

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Appreciate it.

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thanks

jolly turret Apr 13, 2018, 7:25 PM

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Where am i going wrong? Z is supposed to equal .8 but i got 8/11 which is 0.73

📎 20180413_122343.jpg

dense zealot Apr 13, 2018, 7:27 PM

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Hi

jolly turret Apr 13, 2018, 7:27 PM

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hi

dense zealot Apr 13, 2018, 7:27 PM

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have you tried row reductions

jolly turret Apr 13, 2018, 7:27 PM

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not sure what that is

dense zealot Apr 13, 2018, 7:28 PM

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inverses?

jolly turret Apr 13, 2018, 7:29 PM

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do you mean like get zeros in the other rows?

dense zealot Apr 13, 2018, 7:29 PM

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No

unborn mist Apr 13, 2018, 7:29 PM

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📎 image.jpg

dense zealot Apr 13, 2018, 7:29 PM

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If u wanna solve a 3x3

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U find the inverse

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Then transpose

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Well I guess there r faster ways

unborn mist Apr 13, 2018, 7:30 PM

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gaussian elim to get 4/5 for z

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your last step is wrong

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if you do r1+r3 you get 1 in the first column third row

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but you set it to 0

jolly turret Apr 13, 2018, 7:39 PM

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oh ok yeah that last step really messed me up

candid vine Apr 13, 2018, 7:41 PM

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I don't understand what you are doing, what is that 4th columnsupposed to represent?

jolly turret Apr 13, 2018, 7:42 PM

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its a system of equations and the 4th column is the = to part like 4x +5y + 6z = 7 ... the 7 would be on the 4th column

candid vine Apr 13, 2018, 7:42 PM

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Oh you write your systems like that, that's weird :o

jolly turret Apr 13, 2018, 7:42 PM

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its just something in math i guess

candid vine Apr 13, 2018, 7:43 PM

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thonker

jolly turret Apr 13, 2018, 7:43 PM

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theyre called matrices

unborn mist Apr 13, 2018, 7:43 PM

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its a linear algebra concept

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of gaussian elimination in matrices

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look up augmented matrices

jolly turret Apr 13, 2018, 7:44 PM

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i shall be back when i fail this next practice example lol

candid vine Apr 13, 2018, 7:46 PM

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thonker

jolly turret Apr 13, 2018, 8:05 PM

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got the next one right panda_happy

jolly turret Apr 13, 2018, 8:52 PM

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Im trying to do 37 but no matter what series of changes i keep getting y as 1.5 but the answers says 3.5 for y

📎 20180413_135027.jpg

candid vine Apr 13, 2018, 9:00 PM

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Line 1 minus Line 3

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You have 2y = 7

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So y = 3.5

jolly turret Apr 13, 2018, 9:01 PM

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im trying to use the matrices though

candid vine Apr 13, 2018, 9:01 PM

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Well you write your matrice, you do line 1 minus line 3

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The method doesn't change

jolly turret Apr 13, 2018, 9:02 PM

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it does

wind igloo Apr 13, 2018, 9:02 PM

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Why don't you show us what you've done?

jolly turret Apr 13, 2018, 9:03 PM

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give me a sec i did the problem multiple times so ill try to separate the work

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📎 20180413_140407.jpg

candid vine Apr 13, 2018, 9:06 PM

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It's just that you wrote 2 instead of -2 in the first matrice (last line, last column)

wind igloo Apr 13, 2018, 9:06 PM

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You made a mistake copying down the right hand column.

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One of those values should be -2

candid vine Apr 13, 2018, 9:07 PM

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Those sorts of mistakes are the worst, you never see them when you make them

wind igloo Apr 13, 2018, 9:08 PM

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Sign errors are some of the hardest errors to catch.

jolly turret Apr 13, 2018, 9:08 PM

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on which set?

wind igloo Apr 13, 2018, 9:08 PM

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If you look at problem 37, you have ... = 5, ... = 2 and ... = -2

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But your right hand columns in the top line do not contain -2.

jolly turret Apr 13, 2018, 9:09 PM

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oh my god

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i made the same mistake on my first attempt when i wrote the second set smh

true vigil Apr 13, 2018, 9:10 PM

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double check when you copy stuff

jolly turret Apr 13, 2018, 9:11 PM

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its funny because i usually get more errors on that kind of stuff than anything else

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by the way gator would you if you add line 1 to line 3 get 2x + 2y = 7?

wind igloo Apr 13, 2018, 9:15 PM

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2x+2y = 3

jolly turret Apr 13, 2018, 9:15 PM

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oh wait nvm i see now

wind igloo Apr 13, 2018, 9:15 PM

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Err. 2x + 2z = 3

jolly turret Apr 13, 2018, 9:15 PM

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its the negative of the 3rd line

wind igloo Apr 13, 2018, 9:15 PM

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Yes

jolly turret Apr 14, 2018, 12:28 AM

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do you guys know if there are solutions when a row in a matrix is 0 = SomeNumber? Normally if its all zeros id say z=z but with this is it just no solution?

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📎 20180413_172916.jpg

unborn mist Apr 14, 2018, 1:01 AM

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inconsistent system

wind igloo Apr 14, 2018, 1:01 AM

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Agreed. There are no solutions.

haughty portal Apr 14, 2018, 1:11 AM

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thonker

dense zealot Apr 14, 2018, 1:35 AM

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GWmythsBlobGlare

jolly turret Apr 14, 2018, 3:47 AM

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sounds good. i was making sure there wasnt something like for dependent systems

sacred eagle Apr 15, 2018, 4:40 AM

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https://gyazo.com/16b09a018e0b7e558a9949782a57e7b5

Gyazo

clever inlet Apr 15, 2018, 4:41 AM

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do you know the identity?

sacred eagle Apr 15, 2018, 4:41 AM

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no

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what identity

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do u mean like

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cos sine sine cos

clever inlet Apr 15, 2018, 4:42 AM

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hmm, does this actually require the identity?

sacred eagle Apr 15, 2018, 4:42 AM

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not sure

clever inlet Apr 15, 2018, 4:42 AM

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i'm pretty sure it does

sacred eagle Apr 15, 2018, 4:43 AM

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how can i solve it though

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after this its gonna ask me for tangent and sine too

dire crypt Apr 15, 2018, 4:43 AM

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hello

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so do you know the identity

sacred eagle Apr 15, 2018, 4:44 AM

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i dont

dire crypt Apr 15, 2018, 4:44 AM

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cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

sacred eagle Apr 15, 2018, 4:45 AM

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do i need to make the triangle and find the missing side for each one

dire crypt Apr 15, 2018, 4:45 AM

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yea, given hypotenuse = 1, sin(a) = 15/17, you can find cos(a)

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etc

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but you have to be careful about the signs of the cosine values

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for example

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if sin(a) = 15/17, and a is in quadrant I

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will cos(a) be positive or negative?

sacred eagle Apr 15, 2018, 4:46 AM

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mnissing isde is 8

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it will be positive

dire crypt Apr 15, 2018, 4:47 AM

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so if the missing side is 8, what is cos(a)?

sacred eagle Apr 15, 2018, 4:47 AM

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all are positive in 1st quadrant

dire crypt Apr 15, 2018, 4:47 AM

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yea

sacred eagle Apr 15, 2018, 4:47 AM

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8/17

dire crypt Apr 15, 2018, 4:47 AM

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yep

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seems like you have a fine hold of the problem. any other questions?

sacred eagle Apr 15, 2018, 4:49 AM

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whats the next step ?

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is it just

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8/17 + 7/25

dire crypt Apr 15, 2018, 4:49 AM

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well, to find cos(a+b)

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you use the formula

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that

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cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

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so you can substitute the values you have for cos(a), sin(a), cos(b), and sin(b)

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remember

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cos(a+b) does not equal cos(a) + cos(b)

sacred eagle Apr 15, 2018, 4:51 AM

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8/17 x 7/25 - 15/17 x 24/25

dire crypt Apr 15, 2018, 4:52 AM

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yep

sacred eagle Apr 15, 2018, 4:53 AM

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200/425 119/425 -

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is that

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right so far ?

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i havent solved something like this before so

dire crypt Apr 15, 2018, 4:54 AM

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I think you multiplied the numerators incorrectly

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&& \frac{8}{17} \cdot \frac{7}{25} = \frac{56}{425} and -\frac{15}{17} \cdot \frac{24}{25} = -\frac{360}{425} $$

sacred eagle Apr 15, 2018, 4:56 AM

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is it just 8 x 7 ?

dire crypt Apr 15, 2018, 4:56 AM

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[(8 x 7) - (15*24)]/425

sacred eagle Apr 15, 2018, 4:56 AM

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$$ \frac{8}{17} \cdot \frac{7}{25} = \frac{56}{425} and -\frac{15}{17} \cdot \frac{24}{25} = -\frac{360}{425} $$

granite stirrupBOT Apr 15, 2018, 4:56 AM

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📎 latex.png

dire crypt Apr 15, 2018, 4:57 AM

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(56-360)/425

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-304/425

sacred eagle Apr 15, 2018, 4:57 AM

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wait

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wahts 56 - 360

dire crypt Apr 15, 2018, 4:57 AM

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-304

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so some important identities to know are sin(a+b)=sin(a)cos(b) + sin(b)cos(a)

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and the one for cosine

sacred eagle Apr 15, 2018, 4:59 AM

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oh i understand how u got the answer now

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but it says its wrong when i entered it

dire crypt Apr 15, 2018, 4:59 AM

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for cos(a+b)?

sacred eagle Apr 15, 2018, 4:59 AM

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yeah

dire crypt Apr 15, 2018, 4:59 AM

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you typed only 304, right? not -304 (since it puts the negative there for you)

sacred eagle Apr 15, 2018, 4:59 AM

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i tested both

dire crypt Apr 15, 2018, 4:59 AM

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ohh

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it says that b lies in quadrant II

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sorry

sacred eagle Apr 15, 2018, 5:00 AM

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what does that do

dire crypt Apr 15, 2018, 5:00 AM

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so the cos(b) should be negative

sacred eagle Apr 15, 2018, 5:00 AM

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so its 416/425 ?

dire crypt Apr 15, 2018, 5:01 AM

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well -416/425

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but yea, you would type 416

sacred eagle Apr 15, 2018, 5:01 AM

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it doesnt put negative for me

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i have to do the -

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ok it worked

dire crypt Apr 15, 2018, 5:02 AM

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alright sweet

sacred eagle Apr 15, 2018, 5:02 AM

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what is the identity for sin now ?

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sin ( a + b)

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sin(a+b)=sin(a)cos(b) + sin(b)cos(a)

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ok

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thx

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i saw it up there

dire crypt Apr 15, 2018, 5:02 AM

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if you ever wanted to find them online, you can search angle addition formulas

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also

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since you already know cos(a+b), you could also try to complete the triangle

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but if you did it by completing the triangle, you would have to figure out which quadrant a+b is in

sacred eagle Apr 15, 2018, 5:03 AM

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that seems complicated lol

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im opening paint to draw triangles

dire crypt Apr 15, 2018, 5:07 AM

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you could always just use the sin(a+b) formula

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so that you don't have to figure out the quadrant

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the only reason finding the quadrant is necessary

sacred eagle Apr 15, 2018, 5:08 AM

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yeah im gonna use that

dire crypt Apr 15, 2018, 5:08 AM

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oh alright

sacred eagle Apr 15, 2018, 5:08 AM

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but i draw the triangles so i can figure out the sin and cosine

dire crypt Apr 15, 2018, 5:08 AM

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didn't you already figure them out?

sacred eagle Apr 15, 2018, 5:08 AM

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yeah but i did it all in my head

dire crypt Apr 15, 2018, 5:08 AM

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oh, do you need to show work?

sacred eagle Apr 15, 2018, 5:08 AM

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no

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its just

dire crypt Apr 15, 2018, 5:08 AM

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yea that's fine

sacred eagle Apr 15, 2018, 5:08 AM

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better if i can just look at it than try to remember it

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lol

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is that the quickest way to solve these

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with the indentity ?

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and what is the identity for tan(a + b )

dire crypt Apr 15, 2018, 5:18 AM

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The identity is going to be the fastest

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for tan(a+b)

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well

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I never remember the identity for this one XD

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because usually

sacred eagle Apr 15, 2018, 5:18 AM

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oh it gave it to me

dire crypt Apr 15, 2018, 5:18 AM

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you can just use the fact

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that

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tan(a+b) = sin(a+b)/cos(a+b)

sacred eagle Apr 15, 2018, 5:18 AM

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yeah

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how do i do that lol

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-416/ 425 // 87/425

dire crypt Apr 15, 2018, 5:19 AM

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oh

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just multiply by one

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:D

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for gnarly fractions like that

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you can use the property that anything times one equals itself

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like

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2 x 1 = 2

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fancy

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but

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you also know that, for example

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2/2 = 1

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$$ \frac{\frac{-416}{425}}{\frac{87}{425}} $$

granite stirrupBOT Apr 15, 2018, 5:21 AM

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📎 latex.png

dire crypt Apr 15, 2018, 5:21 AM

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so this is the fraction

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and since anything times 1 equals itself

sacred eagle Apr 15, 2018, 5:21 AM

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so -416 / 87 ?

dire crypt Apr 15, 2018, 5:21 AM

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yea

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just multiplying numerator and denominator by 425 (aka multiplying the entire thing by 1)

sacred eagle Apr 15, 2018, 5:22 AM

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it says its wrong

dire crypt Apr 15, 2018, 5:22 AM

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uh

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and 87/425 is indeed correct for sin(a+b)?

sacred eagle Apr 15, 2018, 5:23 AM

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yes

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do i need to take off the negative sing for tan

dire crypt Apr 15, 2018, 5:23 AM

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oh shoot

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you did cos(a+b)/sin(a+b)

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instead of sin(a+b)/cos(a+b)

sacred eagle Apr 15, 2018, 5:23 AM

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what do u mean

dire crypt Apr 15, 2018, 5:23 AM

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keep the negative sign

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I mean

sacred eagle Apr 15, 2018, 5:24 AM

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i did the identity for each one

dire crypt Apr 15, 2018, 5:24 AM

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sin(a+b) = 87/425

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cos(a+b) = -416/425

sacred eagle Apr 15, 2018, 5:24 AM

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yes i got those correct

dire crypt Apr 15, 2018, 5:24 AM

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tan(a+b) = sin(a+b) / cos(a+b)

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so it should be

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$$ \frac{\frac{87}{425}}{\frac{-416}{425}} $$

granite stirrupBOT Apr 15, 2018, 5:25 AM

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📎 latex.png

sacred eagle Apr 15, 2018, 5:25 AM

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is that 87/-416

dire crypt Apr 15, 2018, 5:26 AM

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yea

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remember

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you can take the negative sign up to the numerator

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by multiplying numerator and denominator by -1

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just a by the way sorta thing

sacred eagle Apr 15, 2018, 5:26 AM

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so it should really be -87/416 ?

dire crypt Apr 15, 2018, 5:27 AM

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yea, they're the same thing, but it's more common to put the negative sign in the numerator

sacred eagle Apr 15, 2018, 5:27 AM

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oh ok

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that worked

dire crypt Apr 15, 2018, 5:28 AM

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did everything make sense?

sacred eagle Apr 15, 2018, 5:28 AM

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yes

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i can do these now

dire crypt Apr 15, 2018, 5:28 AM

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if you want, I can show you how the cos(a+b) formula was derived

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kinda fun 😄

sacred eagle Apr 15, 2018, 5:28 AM

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yes i want to

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but

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first i need to finish this homework

dire crypt Apr 15, 2018, 5:28 AM

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alright

sacred eagle Apr 15, 2018, 5:28 AM

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its taking me like 3 hrs now

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im on question 11 out of 30

dire crypt Apr 15, 2018, 5:29 AM

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aw

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well

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I mean one problem at a time

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you got dis

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I'm going to go now though, sorry :/

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good luck though

sacred eagle Apr 15, 2018, 5:37 AM

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alright

finite crescent Apr 16, 2018, 1:50 AM

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📎 Untitled.png

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I'm not sure what I'm doing wrong for this problem. My understanding of the definition of the secant line is that it is just the line between two points of a function.(edited)
My understanding to find the solution to this problem is y = 42 * ((heartbeats at t - 2936)/t - 42)
but the website doesn't like my answers

haughty thicket Apr 16, 2018, 2:28 AM

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Your first one should be

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=tex \frac{2936-2804}{42-40}

granite stirrupBOT Apr 16, 2018, 2:29 AM

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📎 latex.png

haughty thicket Apr 16, 2018, 2:29 AM

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That is the slope of the tangent line

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Which is the same as the slope of the secant line

finite crescent Apr 16, 2018, 3:05 AM

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Huh, that's what I have and it doesn't accept it. 1

wind igloo Apr 16, 2018, 3:43 AM

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The numbers shown in the image are not what @haughty thicket has calculated.

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The calculation above gives, approximately, 66 beats/min

opaque parrot Apr 16, 2018, 9:36 AM

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can anyone suggest me good website for learning function sketching?

meager nymph Apr 17, 2018, 4:51 PM

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I’m on 4. The answer is going to be in fractions like is for the example problem at the top of the pic. I can also show an example problem if that helps. I am confused when sliding everything to one side and then the factoring.

📎 image.jpg

hexed ermine Apr 17, 2018, 8:54 PM

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Make everything in terms of sin first

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And factor out a 2 on RHS

eternal solstice Apr 17, 2018, 9:44 PM

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Hey guys. I've been grinding out some homework all day and got stuck on this problem. Can anyone point me in right direction?

📎 Screen_Shot_2018-04-17_at_2.41.38_PM.png

storm stirrup Apr 17, 2018, 9:44 PM

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ayyyy general solutions

eternal solstice Apr 17, 2018, 9:45 PM

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I know that I can use the double- angle formula to turn it into 16sin(x)cos(x)+15sin(x)=0

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Do i combine like terms?

storm stirrup Apr 17, 2018, 9:46 PM

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Let me quickly do it

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Then I'll come back to u

eternal solstice Apr 17, 2018, 9:46 PM

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Thanks

storm stirrup Apr 17, 2018, 9:49 PM

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Oh cool it's asking for non exact answers

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Phew

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blobsweats

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So yeah getting to 16sin(x)cos(x) + 15sin(x) = 0 is correct

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You just have to factor out sin(x)

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So you get sinx(16cosx + 15) = 0

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This is true when either sin(x) = 0

eternal solstice Apr 17, 2018, 9:50 PM

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Ok

storm stirrup Apr 17, 2018, 9:50 PM

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or 16cos(x) + 15 = 0

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Go from there, if you get stuck just shoot. List your solutions here before you input them

eternal solstice Apr 17, 2018, 9:51 PM

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So i need to solve for x for the last solution?

storm stirrup Apr 17, 2018, 9:52 PM

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In both

eternal solstice Apr 17, 2018, 9:52 PM

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Ok. Thanks for pointing me in the right direction. Let me try and figure the rest out.

storm stirrup Apr 17, 2018, 9:53 PM

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Make sure you find ALL solutions between 0 and 2pi, you should have 4

eternal solstice Apr 17, 2018, 9:55 PM

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@storm stirrup Ok so I know that sin is 0 at 0, and pi

storm stirrup Apr 17, 2018, 9:56 PM

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tep

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yep

eternal solstice Apr 17, 2018, 9:56 PM

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but I'm blanking on how to find the other two values. cos(x)=-15/16

storm stirrup Apr 17, 2018, 9:56 PM

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So for the other two values

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The first one you can find by simply putting in your calculator arccos(-15/16)

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Make sure you're in radians

eternal solstice Apr 17, 2018, 9:57 PM

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ok I got 2.786

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arccos is the samething as cos^-1 right?

storm stirrup Apr 17, 2018, 9:58 PM

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yeah

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Just a different way of writing it

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Do you have or know a formula for general solutions?

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📎 general_solutions.PNG

eternal solstice Apr 17, 2018, 9:59 PM

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+2pi n ?

storm stirrup Apr 17, 2018, 9:59 PM

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Because you're dealing with cos(x)

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You have cos(x) = cos(2.786)

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And because trigonometric functions are cyclic, you can use the general solutions formula for cosine

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so x = 2n(pi) +- 2.786

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You just have to find the integer(s) "n" that make x between 0 and 2pi

eternal solstice Apr 17, 2018, 10:01 PM

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So i could subtract?

storm stirrup Apr 17, 2018, 10:01 PM

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yeah

eternal solstice Apr 17, 2018, 10:01 PM

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2n(pi)-2.786?

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because if I add, it would put me over 2pi

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ok

storm stirrup Apr 17, 2018, 10:03 PM

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yeah

eternal solstice Apr 17, 2018, 10:04 PM

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Still cant figure out that number.

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357.21?

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Nvm nvm nvm

storm stirrup Apr 17, 2018, 10:05 PM

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Well the only two values of n that allow for an x between 0 and 2pi are n=1 and n=0

eternal solstice Apr 17, 2018, 10:05 PM

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I thought i could do 360- the value

storm stirrup Apr 17, 2018, 10:06 PM

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Yeah stay in radians

eternal solstice Apr 17, 2018, 10:06 PM

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but i had to do 2pi-2.786

storm stirrup Apr 17, 2018, 10:06 PM

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yep

eternal solstice Apr 17, 2018, 10:06 PM

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Great. Thanks for the help.

storm stirrup Apr 17, 2018, 10:06 PM

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So what are your 4 solutions?

eternal solstice Apr 17, 2018, 10:06 PM

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I was stuck on that for quite a while.

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0, pi, 2.786, 3.5

storm stirrup Apr 17, 2018, 10:07 PM

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Yep

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To 2d.p. they would be 0.00, 2.79, 3.14, 3.50

eternal solstice Apr 17, 2018, 10:08 PM

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Very helpful. Thank you.

dense trellis Apr 17, 2018, 11:16 PM

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how do you find the inital speed of a function

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for example

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https://gyazo.com/46bc80032aea7565bbfd678c43b83a9a

Gyazo

earnest sable Apr 17, 2018, 11:18 PM

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initial speed of a function?

bold isle Apr 17, 2018, 11:22 PM

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Mmmmmm are you talking about integrals and that such?

hexed ermine Apr 17, 2018, 11:28 PM

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Probably if you are talking about time being as x values; at when x=0

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So at 7

bold isle Apr 17, 2018, 11:29 PM

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@dense trellis show us the complete problem

dense trellis Apr 17, 2018, 11:38 PM

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its literally that function and it was in a test involving rate of change and instataneous and stuff

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and it asked for the initial speed

bold isle Apr 17, 2018, 11:43 PM

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i agree with PJS in any case 😅

lucid spindle Apr 18, 2018, 9:25 AM

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-9,8x+13,4

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Fill in x 0

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You get 13,4

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Thats the initial speed

rocky bison Apr 18, 2018, 9:41 AM

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but what is that function is speed and not displacement thonker

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It's too ambiguous

earnest sable Apr 18, 2018, 11:33 AM

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@lucid spindle thats only the vertical speed

lucid spindle Apr 18, 2018, 11:34 AM

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Isnt that what they asked for?

earnest sable Apr 18, 2018, 11:35 AM

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they asked for the initial speed
they equation they gave is y=f(x)

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you would initially have to find the 2 equations x = f(t) and y = f(t) and then sub one into the other to get y = f(x)

rocky bison Apr 18, 2018, 4:28 PM

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How is that just vertical speed?

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He took a differential of the graph which I assumed was based on the idea it's a displacement function

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@earnest sable

wind igloo Apr 18, 2018, 4:46 PM

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Meh. It's a poorly-framed question.

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The form of the equation, f(x) = -4.9x^2 + 13.4x + 7 -suggests- that it ought to be displacement as a function of time.

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Because -4.9 is -9.8/2, which happens to be the acceleration due to gravity in m/s^2

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That said, Dusty isn't wrong in that it only accounts for vertical displacement.

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There is, however, no information given on what, if any, horizontal displacement/velocity/acceleration there is.

jolly olive Apr 19, 2018, 3:23 AM

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A particle is moving along the curve y^2 − 6x^4 = y. At the moment when x = −1 the x-coordinate is increasing at the rate of 5 cm/sec. If the y-coordiante is negative at this moment, is y increasing or decreasing?How ast?

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anyone know how to solve this

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all i know is i need to take the derivative implicitly

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nvm found a khan academy vid on how to do it

calm thicket Apr 22, 2018, 10:59 PM

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What is a "Trace" of a matrix? When and why would we need it?

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I can google pretty easily to find it's the sum of the diagonals, but that doesn't tell me what it represents geometrically or answer the second question.

eternal solstice Apr 22, 2018, 11:57 PM

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Hi guys. Anyone available for some quick trig help?

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📎 Screen_Shot_2018-04-22_at_4.56.35_PM.png

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I know how to replace the sin^2 with cos^2, and I know how to factor the equation. I get cos=-3/4 and cos = 1/2

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I also know the values of cos = 1/2 between 0 and 2pi. But i struggle understanding how to figure out the values of cos=-3/4 over two pi.

earnest sable Apr 23, 2018, 12:03 AM

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can't you just do arccos(-3/4) forthat?

eternal solstice Apr 23, 2018, 12:03 AM

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Yeah I can gives me the correct value in the QII

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Now I need to find the value in QIII

earnest sable Apr 23, 2018, 12:04 AM

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QIII?

eternal solstice Apr 23, 2018, 12:04 AM

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quadrant 3

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Nvm. I think I figured it out. I was over thinking it.

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take the value and subtract it from 2pi

hexed ermine Apr 23, 2018, 12:05 AM

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Yep

eternal solstice Apr 23, 2018, 12:05 AM

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or add pi/2

viscid thistle Apr 23, 2018, 12:06 AM

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For anyone interested, I spent some time on Desmos making an interactive Unit Circle

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https://www.desmos.com/calculator/mgjsh2vwaz

Desmos Graphing Calculator

Improved Unit Circle

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You can play around with it if you want

eternal solstice Apr 23, 2018, 12:07 AM

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Damn. That is pretty cool.

viscid thistle Apr 23, 2018, 12:07 AM

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Ty

hexed ermine Apr 23, 2018, 12:07 AM

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👍🏼

eternal solstice Apr 23, 2018, 12:19 AM

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Okay basic question. I need to distribute 3(2sinxcosx)

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would it be 6sinxcosx or 6sinx3cosx

viscid thistle Apr 23, 2018, 12:20 AM

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Treat sin x and cos x as if they were just variables

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It would be 6 sin (x) cos (x)

eternal solstice Apr 23, 2018, 12:20 AM

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okay thanks

viscid thistle Apr 23, 2018, 12:20 AM

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np

eternal solstice Apr 23, 2018, 1:16 AM

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Okay. Why can't I get this right? Dont i just do arcsin(-.45) and add pi/2?

📎 Screen_Shot_2018-04-22_at_6.15.26_PM.png

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arcsin(-.45) = -.4668

wind igloo Apr 23, 2018, 1:30 AM

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=tex sin\bigg(\frac{\pi}{2} + x\bigg) \neq sin(x)

granite stirrupBOT Apr 23, 2018, 1:30 AM

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📎 latex.png

viscid thistle Apr 23, 2018, 1:33 AM

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I hate how they use x there

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Should be theta

wind igloo Apr 23, 2018, 1:33 AM

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Eh.

eternal solstice Apr 23, 2018, 1:34 AM

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so replace the x in that equation with -.4668?

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I'm confused.

viscid thistle Apr 23, 2018, 1:35 AM

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Oh I see

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It has to do with the Unit Circle

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The graph I sent up in chat has some explanation

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Do you have it open?

eternal solstice Apr 23, 2018, 1:36 AM

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yeah

wind igloo Apr 23, 2018, 1:36 AM

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No. That's a Not Equals sign.

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You want this:

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=tex sin(x) = sin(\pi-x)

granite stirrupBOT Apr 23, 2018, 1:37 AM

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📎 latex.png

viscid thistle Apr 23, 2018, 1:37 AM

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Ok so do you know how sine and cosine correspond with the Unit Circle?

eternal solstice Apr 23, 2018, 1:37 AM

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yes, cos in the x value, sin is the y value

viscid thistle Apr 23, 2018, 1:37 AM

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Ok so sine can equal -0.45 more than once, yes?

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It equals it twice

eternal solstice Apr 23, 2018, 1:38 AM

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yes

viscid thistle Apr 23, 2018, 1:38 AM

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Try and visualize that

eternal solstice Apr 23, 2018, 1:38 AM

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ok sin is negative in the 3rd and 4th quadrant

viscid thistle Apr 23, 2018, 1:38 AM

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Yep

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So since it's a circle, what's significant about these two values?

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Hint: I'm talking about the x-coords

eternal solstice Apr 23, 2018, 1:39 AM

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I'm not sure

viscid thistle Apr 23, 2018, 1:39 AM

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They're opposites of each other

eternal solstice Apr 23, 2018, 1:39 AM

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oh yeah

viscid thistle Apr 23, 2018, 1:40 AM

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For example in another problem one would be x = 1/2 and the other would be at x = -1/2

eternal solstice Apr 23, 2018, 1:40 AM

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ok yes

viscid thistle Apr 23, 2018, 1:41 AM

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Hold on, no it's asking for the angle in radians not the x coordinate.

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Damnit

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Ok so you want to find arcsine (-0.45)

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And that's one of your answers

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You still here?

eternal solstice Apr 23, 2018, 1:44 AM

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Yeah I am

viscid thistle Apr 23, 2018, 1:44 AM

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kk

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So find arcsine (-0.45)

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In radians

eternal solstice Apr 23, 2018, 1:44 AM

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I found arc sin(-.45)

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-.4668

viscid thistle Apr 23, 2018, 1:44 AM

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Ok good, but since we want our answer as a positive, what can we add to it?

eternal solstice Apr 23, 2018, 1:45 AM

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pi

viscid thistle Apr 23, 2018, 1:45 AM

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Close, π is only halfway around

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2π

eternal solstice Apr 23, 2018, 1:45 AM

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ohok

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5.8164

viscid thistle Apr 23, 2018, 1:46 AM

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gg

eternal solstice Apr 23, 2018, 1:46 AM

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That answer is correct

viscid thistle Apr 23, 2018, 1:46 AM

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yes

eternal solstice Apr 23, 2018, 1:46 AM

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now i just need to find the other value

viscid thistle Apr 23, 2018, 1:46 AM

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Now we have to find the other

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And I don't think it's the negative of it

eternal solstice Apr 23, 2018, 1:46 AM

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so 5.8164 is in the QIV right?

viscid thistle Apr 23, 2018, 1:46 AM

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Ok I know how to find it but it might be a bit tricky to explain

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yes

eternal solstice Apr 23, 2018, 1:47 AM

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can't i just subtract pi/2 from our original answer

viscid thistle Apr 23, 2018, 1:47 AM

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Anything greater than 3π/2 is in quadrant IV

eternal solstice Apr 23, 2018, 1:47 AM

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because i need QIII

viscid thistle Apr 23, 2018, 1:47 AM

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No, you could only subtract π/2 if theta was halfway through Quadrant IV

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(315 degrees)

eternal solstice Apr 23, 2018, 1:48 AM

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hmm

viscid thistle Apr 23, 2018, 1:48 AM

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I'll make a visual

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📎 image.jpg

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The shaded areas are the same area, just mirrored across the y-axis

eternal solstice Apr 23, 2018, 1:50 AM

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ok

viscid thistle Apr 23, 2018, 1:51 AM

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So what we want to do to find the question mark is subtract 5.8164 from 360 degrees or 2π to get the shaded angle

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And then add that value to π

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Can you visualize why that works?

eternal solstice Apr 23, 2018, 1:52 AM

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Yeah that helps

viscid thistle Apr 23, 2018, 1:52 AM

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Ok so

eternal solstice Apr 23, 2018, 1:52 AM

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So i got .4667

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pi

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3.6083

viscid thistle Apr 23, 2018, 1:52 AM

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(2π - 5.8164) + π

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Yeah let me get my calculator lol

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Yep I got the same

eternal solstice Apr 23, 2018, 1:52 AM

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that is correct

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Thanks for the help

viscid thistle Apr 23, 2018, 1:52 AM

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np

eternal solstice Apr 23, 2018, 1:52 AM

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I really need to get into the habit of drawing

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I'm realizing im much more of a visual learner haha

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so soon as I saw that picture it clicked.

viscid thistle Apr 23, 2018, 1:53 AM

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Visual representations always help, especially when you get into physics

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Yeah me too

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I need a video or a whiteboard in front of me lol

eternal solstice Apr 23, 2018, 1:53 AM

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Lol exactly.

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I really appreciate the help. 👍

viscid thistle Apr 23, 2018, 1:58 AM

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No problem man

gilded marten Apr 23, 2018, 2:06 AM

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I could use some tips if anyone has any

📎 unknown.png

hexed ermine Apr 23, 2018, 2:06 AM

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Some tips would be to determine the amplitude

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and the period of the function

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and if there is any vertical shift or phase shift

gilded marten Apr 23, 2018, 2:07 AM

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A=3 period= 8?

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but would i write it as a cosine or sin?

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and i think it is moved

hexed ermine Apr 23, 2018, 2:08 AM

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Well so far you have 3cos(x)

gilded marten Apr 23, 2018, 2:08 AM

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maybe cos -1

hexed ermine Apr 23, 2018, 2:08 AM

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now the period is 8

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and period is defined as 2pi/b=period

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so 2pi/b=8; solve for b