precalculus

[steep fox]

Oh nvm

I see

Yea, thanks mudkip

[digital rock]

np

[hollow zenith]

Hey, i want to learn Calculus and algebra II what site can I use?

[plain lake]

use khan academy

that's how i self studied calc 1 and it worked pretty well

go algrebra 2-> calc tho and should probs skim over precalc, most stuff there isn't exceptionally important if you're strong with algebra but i believe there is some stuff pretty important for calc

[royal aspen]

to a degree i think you could skip precalc

but precalc helps you significantly understand polynomials

[mortal basin]

Write the series using sigma notation with lower limit n=0.

3+2+7+12+17+⋯+87

a little help on this?

[thick raptor]

I assume the first one is supposed to be -3

and what changes each time?

[mortal basin]

youre adding 5 each time

[thick raptor]

so what's the general term going to look like?

[mortal basin]

3+5n?

[thick raptor]

mmm, but you want to start at -3 for n=0

[mortal basin]

Oh right

so -3+5n

[thick raptor]

yup

Find the upper limit be setting that equal to 87

[mortal basin]

18?

[thick raptor]

uh

== 87+3

[granite stirrup]

90

[thick raptor]

== 90/5

[granite stirrup]

18

[thick raptor]

👍

[mortal basin]

thank you

[thick raptor]

k

[viscid thistle]

Quick question

When would you have to start learning precalc if you want to skip in high school?

Skip all of high school? 👀

no

skip precalc in highschool

[long pond]

Lol

[viscid thistle]

probably 9th or 10th grade then

[hexed ermine]

Ew no, @viscid thistle

No one is as smart as you sir

11th grade is standard for Precalculus

12th grade is calculus

Well 10-11th grade for precal

[long pond]

Well if you want to skip it, you would probably want to start a bit earlier

[thick raptor]

wut

ew

[royal aspen]

@viscid thistle try finding some online class that gives credits and check with your school district if they will accept said credits, (some schools may let you just take the final and then you get the credits but you have to check first before doing anything, and it can be prevented by some beurocratic crap)

[viscid thistle]

@everyone can someone help me with logarithmic eq’s?

[long pond]

@everyone doesn’t work, try @ helpers

Alternatively, you could ask me

[olive briar]

Also why would you ping everyone to help

Coughssss

[viscid thistle]

I need help with Q 10.......anyone.......??

[viscid thistle]

<@&286206848099549185>

It's been more than 30 minutes.... anyone.....??

[earnest stirrup]

@viscid thistle https://qph.fs.quoracdn.net/main-qimg-d8d643cef033a6d306524df0c289df7a.webp

[viscid thistle]

Thanks a lot....!!!!

You saved me my sleep...!!

[drowsy shard]

Do you guys know any good resources for precalc?

I'm taking it over the summer rn, and apparently the summer class is just teaching yourself the concepts

[violet kelp]

@drowsy shard Dont' know if I have any particular resources but you could always ask people here

[viscid thistle]

Very gud that's correct

[plain lake]

khan academy is a useful resource i find

for just about any level math up to diff eq

[viscid thistle]

usually its reliable

[graceful forge]

Can someone help me with function

[long pond]

[graceful forge]

f(x)=5x+9 and g(x)=6−x2, calculate f∘g(−2)

[long pond]

By x2 do you mean 2x or x^2?

[graceful forge]

sorry yes

[long pond]

Umm

which one

[graceful forge]

(x)=5x+9 and g(x)=6−x^2, calculate f∘g(−2)

[long pond]

Ok thanks

What are you having trouble with?

Do you know what ∘ means?

[graceful forge]

this is the answer I got after calculations 78 - 10x^2

here was my calculation 5 (6 - x^2) + 9 (2)

is my formulation wrong?

[long pond]

Well if it’s g(-2), then you want to substitute in -2 for x

You shouldn’t have x’s in your final answer

[graceful forge]

ok I will try that way

thanks

[long pond]

Np

[graceful forge]

😩

still wrong

[long pond]

What did you get?

[graceful forge]

35

[drowsy shard]

That's weird, bc I just did your problem and I got 35 as well 🤔

You find f(g(x)) and then substitute in -2 afterwards right?

And since it's -x^2, substituting in -2 should get you -4, right?

[limber bone]

can i self study calculus ? i am prob strong with algebra and it's summer now but i want to strengthen my knowledge for 11th grade. we take permutation combination sequences and series and then calculus

is khan academy math strong enough for high level math ( up till diff eqs )

cuz it's summer and i cant get any schooling for now

[wind igloo]

Khan Academy won't hurt.

[limber bone]

is it enough alone or do i need other resources?

[long pond]

Have you considered taking an online course, or perhaps a course at a community college?

[limber bone]

i cant atm

something like khan is good but is the knowledge strong enough?

[wind igloo]

I haven't watched it myself, so I can't say how rigorous it is.

But several people here have recommended it, so I feel fairly confident it'll at least be a starting point.

[drowsy shard]

Yeah I'd go over the Precalc and Trig sections on Khan Academy

And I'd look up PatrickJMT and Professor Leonard on YouTubr as well

http://tutorial.math.lamar.edu

these notes are useful as well

[night finch]

@drowsy shard try Brian Mclogan on youtube or Udemy and/or the Pecalculus courses on Coursera

Khan-Udemy-Coursera-Edx

the major online resources

Krista King also

[drowsy shard]

Woah thanks @night finch!

[digital rock]

have you managed to factor x^3-y^3?

[spare trail]

Isn't it x^3 - y^3 = (x - y)(x^2 + xy + y^2)

[sage herald]

oops sorry

[spare trail]

But ye wrong signs in any case

[sage herald]

removed it

[spare trail]

so h < a^3 so, h - a^3 < 0

(cube root of h)^3 - a^3 < 0

[digital rock]

I mean I know what it is :^)

[viscid thistle]

👀

[vestal oak]

so what is precalculus?

(we don't have specific math subjects here until university)

(just "mathematics")

[eternal folio]

The same here where I live. I would be interested too.

[vestal oak]

is it just like algebra (the solving linear/quadratic equations kind not the abstract one)?

[lost pawn]

precalculus is building up to learn calc

advanced trigonometry, polynomials and abstract algebra I think

[vestal oak]

when I say abstract algebra I'm referring to things I don't really understand cause it's second year stuff here, after you've already had a year of linear algebra and analysis

so I kinda doubt it'll be thay

[lost pawn]

Well i mean

[vestal oak]

I don't exactly know what that class covers though

[lost pawn]

Calculus is a part of analysis, no?

[vestal oak]

yea

our curriculum went sth like... (starting at the beginning of high school)
solving systems of linear equations
solving quadratic equations/finding roots of second order polynomials
bunch of trig
bunch of probability
some vector geometry
differentiation
integration

I'm missinf stuff cause it's been a while

but those are the most important things I can think of

high school math was no proofs, university was basically only proofs, assuming but not actually requiring you to hsve seen the high school stuff

[plain lake]

that's basically precalc

here you also do some basic analytical geometry with conics

[glossy rover]

Can anyone be of assistance?

[viscid thistle]

That looks right

[gritty blaze]

Question 6 ?

[viscid thistle]

Aue

Aye

Nvm

[glossy rover]

Yeah question 6

I’m having trouble

[fading token]

Draw a unit circle

[glossy rover]

I mean I have that

It’s just looking at the clock in clock wise way

[fading token]

In a unit circle, the angle increases in a counter-clockwise way

[gritty blaze]

$$\cos(\theta - \pi) = -\cos(\theta)$$\$$\sin(\theta - \pi) = -\sin(\theta)$$.

[glossy rover]

ok so

-pi/3 would be where 11pi/6 would be right

[hexed ermine]

No

-pi/3+2pi -> -pi/3+6pi/3 = 5pi/3

[viscid thistle]

@glossy rover remember that a full revolution around the unit circle is 2π

Since we can work with positive radians much better, you can add or subtract 2π to theta and still get the same trig function values

[mortal basin]

how do you form sin equations from amplitude period and a point?

[wind igloo]

y = A sin(wt + k)

A is your amplitude, w controls the period, and k will let you hit a specific point.

[long pond]

Just an added note, k also determines how the graph is shifted horizontally.

[grim current]

A basic trigonometric question. What is the reason to restrict the range of values in inverse trigonometric functions?

Is it related to the symmetry of angles of left and right sides in the trigonometric circle that have the same sin?

[long pond]

Well, if you take sin for example, it’s a periodic function, right? Meaning multiple x values output the same y values

However, the definition of a function prohibits multiple y values corresponding to one x value, so arcsin(x) is only defined from -pi/2<=x<=pi/2

Other wise, there would be an infinite amount of outputs for one input, say 0

=tex \sin(\theta+\pi\cdot k)=0

[long pond]

Sorry about that

[grim current]

Ah, I see. So, it would be for example, a non-injective function, with multiple values of x with the same y?

[long pond]

Wait. Isn’t an injection function a one-to-one function?

Injective*

[grim current]

Yes, that is why I said opposite.

[long pond]

Oh sorry I thought you meant opposite as in inverse

Then yes

[grim current]

In this case, I didn't articulate very well.

Actually I meant non-injective function.

[long pond]

Yes.

For example, the inverse of x^2 does not have a complete inverse because it is non-injective

[grim current]

Hm.

That holds the reason why every inverse function is bijective.

[long pond]

t!wiki bijective

[brisk mica]

📖 | ** https://en.wikipedia.org/wiki/Bijection **

[long pond]

I would google it but I’m lazy

Wow I had no idea all those terms existed

[grim current]

Haha.

It is a function that is both injective and surjective.

So as a result, it is bijective.

Anyway, thanks for your help, I appreciate it. ^^

[long pond]

Np

[torn nebula]

anyone knows what 5 is? its not absolute value though

[tulip echo]

floor function maybe?

[vestal oak]

just looking at wikipedia, it might be floor or round

it’s apparently used for both

[torn nebula]

I have no idea what that means

[plain lake]

if it's precalc it's probs not a floor/ceiling function

also it doesn't really look like one

[vestal oak]

floor means … well it means one of two different things:
•either it’s the largest integer n with n≤x (so floor(4.5) = 4, floor(-3.5) = -4)
•or it’s just the number with the decimals chopped off, so floor(4.5) = 4, but floor(-3.5) = -3

round means, well, rounding to the nearest whole numbers

[viscid thistle]

Or it might just be brackets

[drowsy shard]

My precalc textbook has this function in it; it's prob a floor/greatest integer function

https://m.youtube.com/watch?v=UQ3a2QH_-GU

Heres a link explaining them

[torn nebula]

thank you!

does the graph of y=secx have a symmetry or an inverse

[young lintel]

graph it on desmos and use line test lel

[viscid thistle]

=pup 5(-7/5)^2+2(-7/5)

[granite stirrup]

Do more with Wolfram|Alpha pro

Query made by

@tired thunder

[viscid thistle]

=pup (5(-7/5)^2)+(2(-7/5))

[granite stirrup]

Do more with Wolfram|Alpha pro

Query made by

@tired thunder

[graceful forge]

hi guys

What is the Absolut extrema

how do you find one

[eternal folio]

You find the the local extrema and then you find the most "extreme" of them.

[graceful forge]

on the vertex formula (h, k) is the absolute extrema is always k?

not sure

[eternal folio]

You mean: f(x) = (ax + h)^2 + k?

But yes, if k is the thing that you add to the squared term, then yes, that is the one and only extremum.

Therefore it is the absolute extremum.

[dense zealot]

a(x-h)^2 + k child smh

[faint peak]

is anyone here

[viscid thistle]

you are

[long pond]

[elfin dagger]

sometimes I

[viscid thistle]

[faint peak]

or how to find points out of a refrence angle

[patent beacon]

@faint peak
Are you asking how to calculate sin(x) and cos(x)?

[radiant verge]

Help please

[turbid torrent]

So the x coordinate is 2, and the y coordinate is -3

so $$\cos \theta = 2 $$ and $$\sin\theta = -3 $$

[vestal oak]

uh, no

that’s only valid if the point is on the unit circle, which it isn’t

need to divide by the radius

x = r*cosθ

so cosθ = x/r

(where r = √(x² + y²))

[viscid thistle]

$$\cos \theta = \frac{2\sqrt{13}}{13}

$$\cos \theta = \frac{2\sqrt{13}}{13}$$

[viscid thistle]

$$\csc \theta = \frac{-\sqrt{13}}{3}$$

[viscid thistle]

hmm

just a minute

$$\tan \theta = \frac{-3}{2}$$

[clear coral]

What's the best way I could prepare for Precal over the summer so I don't get shredded during school?

I'm also learning it for Competition math as well, so would the AOPS Precalculus book be fine?

[true vigil]

I think so

competition math is usually much harder than school math

so that should be fine

[viscid thistle]

You don’t need precalc for competitions

[clear coral]

AMC 12 and AIME involve a bit of precal, just no calculus

[granite stirrup]

Rendering failed. Check your code. You can edit your existing message if needed.

[granite stirrup]

Rendering failed. Check your code. You can edit your existing message if needed.

[viral lynx]

[viscid thistle]

I mean

It’s really basic knowledge of precalc at most

[viscid thistle]

As a calc student I feel stupid asking questions here but... does tan(x) have amplitude?

I don't think that the coefficient in front of the entire trig function would be the said "amplitude" considering tangent's range is from negative infinity to positive infinity

In the function f(x) = Atan(B(x - C)) + D, what would A be if it isn't amplitude?

Just a vertical scale factor?

This is less mathematical and more dictionary definition

[viral lynx]

yeah it's just a scale factor

amplitude only really makes sense if there's a maximum value that it oscillates to

[viscid thistle]

True, I guess that only applies to sine and cosine

[viral lynx]

but tan covers all of the real numbers in its output so it doesnt have the same oscillating stuff that sin and cos do

yea

i mean you wouldnt really talk about the amplitude of any other function like x^2

the question of amplitude only really means anything for sin and cos (and i guess related things like complex exponential functions and whatnot)

[viscid thistle]

Well, that helps. My Desmos graph is now complete haha

Feel free to test it out

https://www.desmos.com/calculator/jrvgqbhb68

[viral lynx]

ah that's neat

[earnest wedge]

Can anyone help me with precalc?

I do not understand this at all as the teacher does not teach it very well as they expect us to know this but really it's just hard to study and learn
https://cdn.discordapp.com/attachments/379714215079968772/461993791776096266/image.jpg
https://cdn.discordapp.com/attachments/379714215079968772/461993842908856320/image.jpg
https://cdn.discordapp.com/attachments/379714215079968772/461993974152953876/image.jpg

[viscid thistle]

ok which problems? @earnest wedge

[earnest wedge]

I don't understand how to solve like the inverse trig functions, algebraic equations and the calculator part

[viscid thistle]

how well do you know the unit circle?

[earnest wedge]

not really well

but ik how to get the values from it

[viral lynx]

you really only need to know your special right triangles (30-60-90 and 45-45-90) to get the unit circle values

[earnest wedge]

oh okay

[viral lynx]

i still don’t have the circle completely memorized; i just got really quick with the triangles

you still have to be familiar with it and able to reason through everything, but you don’t need to memorize every trig function at every angle separately

it’s all built off the two triangles

[earnest wedge]

oh okay..

that sucks

but it is what it is

im not good at reasoning

which is the tricky part

[viral lynx]

ah yeah

tbh just practice until you get more comfortable with it

it’s a pain to force yourself to do work but it really pays off

all you really need to know is that the quadrant gives you the sign of the sin/cos function and then think about how the triangle is rotated for a given angle

[earnest wedge]

no you don't understand..

I'm taking like um.. summer school and each day we are given a quiz which reflects our grade then a final unit test

its like the cheapest grading system

;-;

[viral lynx]

rip

[earnest wedge]

so I'm not sure what i can do

since idk how to do this stuff

and tried looking for resources

[viscid thistle]

that should help

pages 3 and 4 mainly

[earnest wedge]

oh okay

omg

[viscid thistle]

also, these kinds of problems are a pain to do but just know, the more practice you get, the better you'll be

[earnest wedge]

this has so much

info

ty

[viscid thistle]

so if you hate these, force yourself to do like 20 hard problems and see how you feel

[viral lynx]

smh they don’t even have the triangles

[viscid thistle]

yeah np lmao

lol

[earnest wedge]

crap

;p

the hard one is the tan function

bc they are not even listed as coordinates

so rip

[viral lynx]

tan = sin/cos

which is also the slope of the line at that angle

[earnest wedge]

ok

I need help knowing which quadrants the ranges are for the csc, sec, and cot

[viral lynx]

tan(0) = 0 bc the slope of the line made by a zero degree angle is zero, tan(45) = 1 since the slope of the line made by a 45 degree angle is 1, etc

[earnest wedge]

oh okay

[viral lynx]

and csc = 1/sin, sec = 1/cos, cot = 1/tan so they will have the same sign as the one they’re the flipped version of

that’s something else i guess you need to memorize, the csc <-> sin etc. correspondence

i remember that the ones with co- are paired with one that doesnt

[earnest wedge]

oh oky

I need help with triangle word problems

I'm so bad at them

https://cdn.discordapp.com/attachments/379714215079968772/461993974152953876/image.jpg

[viral lynx]

just the last one or the others too?

[earnest wedge]

the others

wdym by others

[viral lynx]

like are you confident in your answers for 1-3 or did you want me to look at them too

[earnest wedge]

yes

please look at them as well

[viral lynx]

(also you’ve got your name in the pic; idk if you’d want to crop that out)

[earnest wedge]

idrc

[viral lynx]

aight

for #3, you can’t use the pythagorean theorem for triangles that aren’t right triangles

you can use law of sines

but the rest look good, and all the angles you wrote down for #3 check out

[earnest wedge]

law of sines?

wait what's that

[viral lynx]

one thing i’ll mention is that your drawing for the first one isn’t really the right drawing (both measurements are made from the same place) but you did the math right so i’m guessing you just drew it like that to fit the numbers or something

——
oh have you not learned law of sines yet?

wait

sorry i can’t add lmao

it is a right triangle

yeah you got that one right then

[earnest wedge]

wdym

which one

[viral lynx]

#3

[earnest wedge]

oh

[viral lynx]

i was looking at that angle and thought it wasn’t 90 but i just added wrong

so yeah you did everything fine

except for the weird drawing on number 1 but you still did the math right

[earnest wedge]

oh ok

i need help with # 4

[viral lynx]

have you used vectors yet

[earnest wedge]

NO

[viral lynx]

okay there’s another way then

think about the distance the plane covers in 1 hour and draw a triangle for that

like he starts at 0 elevation and climbs to a height h, covering 640 miles along the hypotenuse

and you know the angle he’s climbing at

find the distance along the ground that he covered in that time

and that’s the distance in 1 hour, so you have the mph speed

[earnest wedge]

oh ok

[viral lynx]

(and as a teaser for what you’ll get to do in physics, you can do the exact same triangle with the velocity directly and think about “projecting” the vector down onto the ground and only looking at the bit of his velocity that’s moving him forwards instead of the bit that’s pointed upwards)

[viral lynx]

you can treat it as a right triangle; you want to know the distance along the ground that he covered, and what you have drawn right now has some extra length to it on the ground side

[earnest wedge]

but how would i solve for the ground distance

and it said 14.03 degrees

[viral lynx]

yea he's flying 14 degrees upwards

like the x axis is distance along the ground and the y is height

if i had drawn axes

so you know that in the air—when you consider both his upward and his forward movement—he went 640 mi

[earnest wedge]

yes

[viral lynx]

and you want to figure out how far forward he moved

[earnest wedge]

how do we solve for that though

um

[viral lynx]

you have a right triangle and you know one of the angles for it

[earnest wedge]

law of cosines?

where

[viral lynx]

so if you just went along the ground beneath him you'd walk along the yellow/orange path right

if you walk so that he is flying directly overhead you

and you can place a pole perpendicular to the ground that points straight up at him

so the bottom right angle in my drawing is 90 degrees

and you know he's climbing at an angle of 14 degrees to the ground

so the angle on the left is 14

and it's just socahtoa from there

[earnest wedge]

wdym on the left

angle on the left

[viral lynx]

like where i wrote takeoff

the angle inside the triangle there

[earnest wedge]

ok

idk how we know its a right traingle tho

[viral lynx]

so we know that he is moving both forwards and upwards at the same time right

and the direction "forwards" makes a right angle to the direction "upwards"

[earnest wedge]

oh okay

[viral lynx]

so if we make a triangle where one leg has the full forward length and the other has the full upward length, we know that the legs are at a right angle to each other

yeah

[earnest wedge]

so then

how do I solve it

like

do I just do cos

of 14.03

[viral lynx]

yup

[earnest wedge]

oh

[viral lynx]

so cos is what

[earnest wedge]

= g/640

[viral lynx]

yep!

then isolate g, plug into a calculator if you want or just leave it

[earnest wedge]

do I need inversesymbol

[viral lynx]

nah

cos(14.whatever) is just a constant number

a little less than 1

cos(14) = g/640, so g =640*cos(14), which is probs like 620 or something; i don't have a calculator on me

oh wait

==640*cos(14°)

[granite stirrup]

Tokenization error
On line 1 at position 11

640*cos(14°)
          ^

[viral lynx]

rip

== 640cos(14π/180)

[granite stirrup]

640×cos(7×π/90) = 620.989264816638

[viral lynx]

wow my guess was close

[tall turret]

👀 wats zis?

[viral lynx]

sup solitary

some triangles

[tall turret]

O i see

Physics?

[viral lynx]

nah

[earnest wedge]

why 14Pi/180

[viral lynx]

i had to convert to radians

mathbot only allows radians

[earnest wedge]

oh okay

[earnest wedge]

Welp

I think I failed my quiz

So rip

I felt really bad about it..

[earnest wedge]

it dropped my grade down to a D

welp

[long pond]

😬

[earnest wedge]

;-;

[viscid thistle]

Don't worry

If you get 0%, your next test score will literally be a million times better.

[thick raptor]

@viscid thistle a million times 0 is still 0

[viscid thistle]

That's the joke

¯_(ツ)_/¯

[thick raptor]

🤦

[worthy summit]

Ehm million times 0 is still 0 😣

[rocky bison]

@viscid thistle what is ohotnik

[tall granite]

pretty sure it means hunter

[earnest wedge]

Does anyone want to help review and practice trigonometry of pre calc with me? I don't how I could study for my upcoming test and I need help understanding how to solve problems on my own. It's okay if you do not want to.. and I'll just review on my own.

[long pond]

I might know a server that could help, but they do a lot of calculus as opposed to precalculus

You could try, though

[earnest wedge]

oh okay

[long pond]

Do you want the invite?

[earnest wedge]

sure

[long pond]

https://discord.gg/jJqeMm

There’s not a lot of members, but I think someone might be willing to help

[earnest wedge]

okay

[patent beacon]

@earnest wedge
Feel free to ask any questions you might have in the questions channels as well.

[long pond]

^^

[earnest wedge]

oh okay

[viscid thistle]

Interesting...

[dark tinsel]

Yeah that's just an identity but moved around

[viscid thistle]

I know, I developed it on my free time today

[viscid thistle]

Is this pretty much trigonometry on the server?

I can't find the trig channel so I'll assume this is the closest we'll get

[grizzled hull]

People have used both this and the geometry channel for trig in the past.

Both make sense, really. Trig is a subset of geometry, and it's considered part of a pre-cal course.

[earnest wedge]

I need help reviewing inverse trig and evaluating trig values

[earnest wedge]

@past jay

yo

[earnest wedge]

@grizzled hull

[past jay]

huuuh

@earnest wedge you still here? XD

[earnest wedge]

im in questions

but yet

yes*

[earnest wedge]

@tall turret do you know how to do inverse trig?

[tall turret]

.<

Ofc

Need help?

[earnest wedge]

Yeah..

[tall turret]

U deleted it?

[tall turret]

Wdy want me to do?

[earnest wedge]

Can you explain how to like solve inverse trig functions?

[tall turret]

Nice clock on the top btw 🕥

[earnest wedge]

;p

[tall turret]

Dude

U r askin me to teach u the entire theory

[earnest wedge]

Wdym

[tall turret]

Can you explain how to like solve inverse trig functions?

This takes half n hour to answer

[earnest wedge]

Oh..

[reef dirge]

wdym

depends on your interpretation of that request

you can't "solve" functions

[earnest wedge]

Ok

How to find inverse trig values of functions

@tall turret

[reef dirge]

???

what's am inverse trig value of a function

[earnest wedge]

Oh

Then finding inverses

Sorry.. I don’t know how to do like do this

Like I have to find radians from a inverse trig function

Or like a value

[reef dirge]

depends on what the ratio you have is

special cases are easy

but otherwise you have to use calculators

[earnest wedge]

Ok

[reef dirge]

sometimes it's better to leave it as, say, arctan(3/4)

[earnest wedge]

The teacher doesn’t let use calculators for the problems though

So I’m trying to understand how to do inverse trig

[reef dirge]

special cases probably then, or problems where you don't have to find the actual values

what kinds of problems are they

[earnest wedge]

Oh ok

Like evaluating trig values

Except their inverse functions

@reef dirge

Taking inverse of values to find trig ratios

[reef dirge]

you mean using trig ratios to find angles?

[earnest wedge]

Yes

Specifically radians

Or whatever

[reef dirge]

if you're not allowed to use calculators, it'll probably all be special angles like 30, 45, 60, 90 degrees

[earnest wedge]

Ok

[reef dirge]

so you have to know 1:2:sqrt(3) and 1:1:sqrt(2) triangles

[earnest wedge]

Well I don’t know how to take inverse of functions

[reef dirge]

and just know what the inverse functions mean

ok what does sin(x) mean?

[earnest wedge]

Sin(x) = opp/hyp

[reef dirge]

inverse of sin means sin^-1 (opp/hyp) = x

you put in ratios and you get the angle

as opposed to getting ratios from putting in angles in original functions

[earnest wedge]

Ok

Could you like show me some examples?

sin(x) = y

[reef dirge]

arcsin(y) = x

arcsin = sin^-1 = inverse of sin

just easier to type

[earnest wedge]

Ok

[reef dirge]

sin(30 deg) = 1/2

arcsin(1/2) = 30 deg

tan(45 deg) = 1
arctan(1) = 45 deg

[earnest wedge]

Ok

[reef dirge]

do you get the idea?

[earnest wedge]

Yes

But like for the problems that I have

It’s already in inverse

[reef dirge]

siiiiiggghghhhhh

[earnest wedge]

tan^-1 = (-1/sqrt of 3)

Multiply square root 3

[earnest wedge]

Negative square root of 3

Pi/6 But negative

[reef dirge]

"taking inverses of values to find trig ratios"

I thought you meant stuff like arccos(pi/3)

I said special cases or problems where you don't have to find the values

[earnest wedge]

Oh..

[reef dirge]

these are problems where you don't have to find the values

[earnest wedge]

Sorry

😦

[reef dirge]

actually

nevermind

[earnest wedge]

?

[reef dirge]

these are problems where you evaluate

[earnest wedge]

Ok

[reef dirge]

can you find the trig ratios correctly?

[earnest wedge]

I’m not sure

Because like

[reef dirge]

by the way

sec = 1/cos

csc = 1/sin

not the other way

that's a huge part

[earnest wedge]

Oh ok

[reef dirge]

I think you don't completely understand inverses

[earnest wedge]

Can we go through the problems I have then? Neither do I..

[reef dirge]

here's the idea with trig functions

if you have a right triangle

[earnest wedge]

I know I have to remember trig functions

Or like values

[reef dirge]

knowing one other angle uniquely defines the ratio of side lengths

[earnest wedge]

Except idk what to do when it is inverse

[reef dirge]

don't memorize

bad idea

understand, not memorize

[earnest wedge]

Ok

[reef dirge]

if you know the angle, you can figure out ratios of any two side lengths

[earnest wedge]

Oh ok

True

But like how is that supposed to help me with evaluating inverse trig

If it gives me values that are um.. not in its original value like tangent or cotangent

[reef dirge]

sorry, computer crashed

the other way around: if you know the ratio of any two side lengths of a right triangle, you can figure out the angles.

[earnest wedge]

Okay

So then

@reef dirge can I try them on my own and you can see what I do wrong?

[reef dirge]

sure

that might be easier

[reef dirge]

to find exactly what you're not clear on

[earnest wedge]

So for the first one it’s Pi/3 Bc it’s sin

And it’s in the domain

Then second one is

Negative Pi over 6

Because when rationalized it equals sqrt 3 over 3

Which is a tan ratio

Third one um

Secant of -1

So idk which quadrants it would be located in

@reef dirge I’m stuck on the inverse csc, sec, and cot

[reef dirge]

arccsc x = arcsin(1/x)

think in terms of ratios

[earnest wedge]

Because idk which domains they are in

Ok

1/x but how is that supposed to help

[reef dirge]

sin -> opp/hyp

[earnest wedge]

Yes

[reef dirge]

csc -> hyp/opp

[earnest wedge]

It gave us negative 1 tho

[reef dirge]

arccsc -1 = arcsin -1, right?

here's a nice trick

[earnest wedge]

Yes

I think so

[earnest wedge]

So you set it like 1/sin^-1 x * -1/1

They cancel out

And end up giving you 0..

[reef dirge]

if x = arcsin(-1)

sin(x) = -1

that's how inverses work, right?

[earnest wedge]

Yes

[reef dirge]

so,

at which angle in that circle is the y coordinate -1?

[earnest wedge]

Pi

But like

[reef dirge]

starting counterclockwise from +x

it's not pi

[earnest wedge]

How is it not Pi

[reef dirge]

3/2 pi, or equivalently, -1/2 pi

[earnest wedge]

oh

Ok now I’m confused

We did csc

So like

[earnest wedge]

Ok

Isn’t that like -Pi/2

@reef dirge

[reef dirge]

that's 3/4 of a circle

[earnest wedge]

Ok

I’m still confused by like your explaination

[reef dirge]

oh wait yeah -pi/2

misread, sorry

[earnest wedge]

Ok

So then

I’m not sure exactly where the functions are located for their domains ranges

Bc like sine is -Pi/2 < or = x < or = Pi/2 But so is for cosecant or maybe not..

People keep telling me second and fourth quadrant

And idk what they are referring to

@reef dirge

[fleet granite]

u dont know what are quadrants?

[solemn quest]

Hi ! Im at my precal and if the y or x is not included in an equation is it a function or not ? ( equations such as x = -5 or y = 1/2 )

[reef dirge]

it's not always a function

but they're always equations

t!wiki function

[brisk mica]

📖 | ** https://en.wikipedia.org/wiki/Function **

[reef dirge]

o

[gritty blaze]

$$y=f(x)=\frac{1}{2}$$ is a function but $$x=-5$$ isn't.

[reef dirge]

t!wiki function (mathematics)

[brisk mica]

📖 | ** https://en.wikipedia.org/wiki/Function_(mathematics) **

[reef dirge]

well x = -5 could be a function if x is the output

[rocky bison]

I think that's more of a definition

You're defining x has being -5

a function will do some operation on an input giving a corresponding output

@reef dirge

But at that point you're just getting into pedantic language

and it's just pain

[reef dirge]

a function of y outputting x \shrug

rip

¯_(ツ)_/¯

[rocky bison]

It's not a function of y

That implies if dependant

But it's just a constant :b

[reef dirge]

that's just notational convention

you never know, a problem might be a trap for people now knowing that

[rocky bison]

what

[reef dirge]

problems that try to confuse people by saying stuff like "let f be a function of y"

[rocky bison]

Yeah

Disgusting

But that does mean that the function, f, is dependant on any values of y

[hybrid wave]

any tips on trying to memorize the radians of the unit circle, my mind is set to degrees by default rip

[rocky bison]

What do you mean?

Trying to remember like 90º is pi/2 and stuff?

@hybrid wave

[hybrid wave]

specifically the fractions, I know the main stuff like pi and 2pi

[tall turret]

U need not

Just remember

=tex 2 \pi ^c =360^o

[tall turret]

And

=tex 1^c= \frac{2 \pi^c}{360^o}

[tall turret]

=tex 1^o= \frac{360^o}{2 \pi^c}

[hybrid wave]

lol

my man

[viscid thistle]

Does anyone know how I can offset this? In other words, shift it left, right, up, down, etc

It’s a polar equation

Right now it’s centered at (0, 0) but I want to know if there’s any way to “shift” it. For example if I wanted it to be centered at (1, 0).

<@&286206848099549185>

[thick raptor]

Write it in cartesian

[viscid thistle]

It is a Cartesian coordinate plane, I just have the graph set to that design to make it easier to comprehend

[eternal folio]

@viscid thistle r-1 = theta

[thick raptor]

No, but the equation is in polar form

@eternal folio wtf no

[eternal folio]

Yes.

[thick raptor]

no wtf

That just pushes everything away from (0,0)

they wanna shift it to (1,0)

[eternal folio]

That shifts the starting point to (1,0). But messes up everything else. Sorry. xD

[viscid thistle]

gg

[thick raptor]

🤦

[viscid thistle]

If it’s impossible it’s fine, just would be a good visual to demonstrate going around the Unit Circle more than once

[thick raptor]

._. just put it in cartesian coordinates like I said

[viscid thistle]

How exactly would I do that?

r = θ translates into what x, y coords?

Could become a parametric function

Errr equation not function

[thick raptor]

θ = arctan(y/x) and r = √(x²+y²)

[viscid thistle]

GOT IT

[thick raptor]

:l

[eternal folio]

Arctan only returns angles between -pi/2 and pi/2, doesn't it?

[viscid thistle]

Parametric seems to work

Thx guys!

[thick raptor]

oi!

@tall granite 🗡

[tall granite]

wtf

[thick raptor]

\👀

no u

@tall granite \🗡\🗡\🗡

[tall granite]

oi!

😱

[hexed pulsar]

anyone have any pre calc study guides or anything bc I haven't done math in two years and I transferred colleges and I got placed in Precalculus (from an art school to a regular college) so I really need a refresher loll

pls ping me if you respond aaaaa thank you ❤ ❤

[rocky bison]

@hexed pulsar kahn

[long pond]

https://khanacademy.org/

[hexed pulsar]

thankyou

[solemn quest]

can negative square roots be an answer in functions or is that not allowed , such answers as f(2) = sqrt 2-4 = sqrt -2

[gritty blaze]

Complex analysis ?

[vestal oak]

can negative square roots be an answer in functions or is that not allowed , such answers as f(2) = sqrt 2-4 = sqrt -2
they can if your function is defined that way

your function needs to be defined as having range ℂ, then it’s fine

but if i*sqrt(2) isn’t in the range of the function

then this f(2) would not be well-defined

[frosty kindle]

(In other words, no, unless you're in senior high school or above. Complex numbers are a whole level of weirdness you probably wouldn't get into until after you learn calculus.)

[wide frost]

complex numbers aren't weird...

[hexed ermine]

^

[split valley]

Hey all

How the heck do you evaluate a square root exponent?

Like 2^squareroot of 2?

I can’t seem to figure out how to do that on a graphing calculator, I keep getting 1.41

[wind igloo]

=pup 2^(sqrt 2)

[granite stirrup]

Do more with Wolfram|Alpha pro

Query made by

@wind igloo

[wind igloo]

Try using parenthesis

[viscid thistle]

Ooof

[proud raven]

are there any great ways to remember the sum and difference of ratios other than just memorizing

like cos(a+b) = cosacosb yadda yadda

[hybrid wave]

not really

only thing I would say is sin(a+b) will carry its sign while cos(a+b) is the opposite

tan(a+b) will also carry its sign in the numerator, but will be opposite in denominator

after awhile you get used to it, like distance formula or quadratic formula

[loud laurel]

((x-4)/(x-3))-(x/(x^2-x-6)) on this equation why can't I factor out (x+2). Problem solver apps multiply it out then collect like terms

[hybrid wave]

well, you also have (x-3) on the bottom, photomath naturally assumes you are trying to create a polynomial

you have to use a different app

that's a nasty problem also, lol, might want to split up into 2 fractions

[proud raven]

thanks @hybrid wave

my teacher tried to show us how to derive it but it seems like more work getting used to that than just memorizing it

[hybrid wave]

Yeah, it's the proof that I remember it by, 2 triangles and bisector down the middle, sin(a+b)

just memorize it haha, no derive it once or twice to understand why it is the way it is, and then get on with other stuff

[proud raven]

I will do it 😄

I just found the hexagon trick so I'm excited about that, the actual chugging of information I'm okay with but in this trig class remembering the tools has been the hardest part for me

[hybrid wave]

yep

[bitter parrot]

Ahhh

Sooo, anyone up for some Logs?

I'm probably going at this all wrong, with every way I've tried, but the problem is:

Solve the equation (put your answer in calculator-ready form)
2log x + log 2 = log (3x - 4)

[viscid thistle]

log x^2 + log 2 = log(3x + 4)

log 2x^2 = log(3x + 4)

2x^2 = 3x + 4

[sage herald]

den solve

[viscid thistle]

2x^2 - 3x - 4 = 0

solve the quadratic then check if the solutions to it meet the restrictions

[bitter parrot]

😭 thank you repyh

[viscid thistle]

3x + 4 > 0 and x^2 > 0

np

[loud laurel]

@hybrid wave thanks. Not sure if I understand but this is the original problem

On the part where's it multiplying cound I cancel x+2 instead so it's like this: =tex \frac{(x-4)-x}{x-3}

=tex \frac{(x-4)-x}{x-3}

[loud laurel]

Or is that wrong. Every YouTube video seems to multiply it as well and keep it in two different fractions then combine them. I've tried many apps, tiger algebra, symbolab, math Papa and they all solve it like photomath

[hybrid wave]

Welp

[tall turret]

@loud laurel Ahoy

[thick raptor]

@proud raven personally derive them all from Euler's theorem.

[wide frost]

@proud raven using complex exponentials is a nice way to easily derive them

@thick raptor i guess you meant that by eulers theorem?

[thick raptor]

yeah

[proud raven]

that sounds complicated and worth learning @thick raptor thanks!

[thick raptor]

It certainly is useful, reducing trig into exponential rules

[meager socket]

@proud raven
Look at the plot for cos(x)^2. It looks exactly like (cos(2x)+1)/2 or something like that. You know have the double angle formula for the cosine.
If you derive you get the one for the sine.
Some manipulations give cos(2x)=cos^2(x)-sin^2(x).
What is the formula for cos(x+y)? It has to be consistent with the above. And it primary looks pretty, symmetric, balanced.
So the only sensible guess i see is cos(x+y)=cos(x)cos(y)-sin(x)sin(y).
Then do the same for sin(2x)=2cos(x)sin(x).
This is much quicker than it looks when written out.

[wide frost]

complex exponentials are easier imo

[proud raven]

@meager socket I've been playing with what you said and I don't understand what you mean

are you saying that by graphing you can intuitively figure out where the + and - go in difference identities

[meager socket]

@jan Niku
Hmm, it might just work for me but be a bad way to memorize for others.
The first identity is figured out by graphing. That's the only one.
The sine double angle formula is by taking a derivative of the first identity.
The cosine sum of angles identity is found by intuitively figuring out where things go, including the + and -, sure. BUT NOT GRAPHICALLY.

[brave void]

Okay

I need help with one thing

Lets say I have

Logx +2 =log4

Base of both logs is 10

How would I solve for x

@help

<@&286206848099549185>

[wind igloo]

Rewrite 2 as log(something)

Then use log properties

[brave void]

Okay

log(2)4?

[wind igloo]

No, you want it in the same base, so you can combine.

[brave void]

okay

log10(100)

[wind igloo]

Yes

[brave void]

then we can dump the log symbol

x+100=4

[hollow obsidian]

no

[brave void]

Rip

[hollow obsidian]

you have to combine the logs on one side

[brave void]

Okay

We could subtract

The log 10(100)

[hollow obsidian]

if you have log(a)+lob(b), it is equal to log(ab)

I think

[wind igloo]

No. Think log properties

[brave void]

logx=log(4/100)

no?

[hollow obsidian]

ok that works

[wind igloo]

That works too

[brave void]

What would be the log properties way

[hollow obsidian]

now that the log encompasses everything you can equate what's inside them

[wind igloo]

You did it. You just used a different property than I was thinking of.

[brave void]

Yeah

So x=4/100\

x = 1/25

[hollow obsidian]

well, the way I mentioned above is
log(100x)=log(4)
100x=4
x=1/25

same thing

[brave void]

Okay

That's cool

Tysm mate

[nova cliff]

need help with precalculus pls

[hazy rapids]

hi

so my teacher is about to call me for a DBA

can someone help me

[eternal folio]

Don't ask to ask. @hazy rapids

[proud raven]

how would you solve 2sin(3x)=1 without general solutions

I tried chasing down using a difference identity but it got really messy and not sure that's correct

How do you approach solving something like that when its not just 2 or 1 x actually

[eternal folio]

What do you mean by without general solutions?

[proud raven]

the way symbolab solves is with general solutions is what it calls it

i couldnt find it in my book

[eternal folio]

That just means that you can plug any integer in for n and you'll get a solution.

[proud raven]

is there a name for this kind of problem

[eternal folio]

Trigonometric equation?

[proud raven]

it doesn't explain how they get the pi/18 is where im confused

my book mentions periodicity but it doesn't seem to mention how to solve when its not a single, half, or double angle

am i supposed to do sin(2x+x)=1/2?

[eternal folio]

Uhmm... not really.

[proud raven]

I feel like I'm missing something obvious 😦

[eternal folio]

sin(x) = 1/2
-> x = 30deg + 360deg * k
or
-> x = 150deg + 360deg * k

where k is an arbitrary integer

Savvy?

[proud raven]

but its sin3x=1/2

[eternal folio]

Yes, but do you understand what I wrote?

[proud raven]

oh, yea

[eternal folio]

Okay, then we can use the same reasoning.

sin(3x) = 1/2
-> 3x = 30deg + 360deg * k = pi/6 + 2pi * k
or
-> 3x = 150deg + 360deg *k = 5pi/6 + 2pi *k

rearranging gives
x = 10deg + 120deg * k = pi/18 + 2/3 * pi * k
or
x = 50deg + 120deg * k = 5pi/18 + 2/3 * pi * k

[proud raven]

itd be the same method for any multiple of x?

[eternal folio]

yes

[proud raven]

😮 oh, I guess that is obvious

[eternal folio]

You can even solve sin(x^2 - 5x + 2) = 1/2 with the same technique.

[proud raven]

thanks, I think I might be burnt out

my brain is not helping 😅

I just have to remember not to use difference unless its not a reference angle I guess

[eternal folio]

For something like sin(....) = constant or cos(....) = constant you don't need the angle sum/difference formulas.

[proud raven]

😄 thank you

[proud raven]

This channel is so cozy

[thick raptor]

k

[proud raven]

does no one take precalc or they just go to the wrong channel or what

by cozy i mean dead

[thick raptor]

k

[proud raven]

🤷 don't mind me geez

[thick raptor]

k

[past jay]

So I was brushing up on matrices since we were never really taught them, And I have a question about reaching reduced row echelon form

Why is it that when using an addition or subtraction operation, you have to use an existing row?

[leaden glade]

what else would you use?

[past jay]

Nevermind, answered my own question.

That was a little dumb tbh. XD

[leaden glade]

the stronger idea is that you can row reduce by using any operation that you describe with a matrix multiplying on the left

reducing matrix A means multiplying it by E like so: EA

where E is inversible

[past jay]

You're saying you could essentially create a matrix in such a way it could row reduce in theoretically one step

That makes sense.

I don't know how you'd go about creating such a matrix but

I know you never said "one step" but just that, if you could define any "operation" in that way, then in theory you could combine them all into one.

[leaden glade]

exactly

so you apply the steps E1, E2, E3...

and E = (E3 E2 E1)

[past jay]

associative property, ye

[leaden glade]

seeing elementary row operations as matrices is nice

you can try it as an exercise, to write the elementary row operations as matrices

swapping two rows, adding a row to another one, multiplying a row by x

[past jay]

eh.. maybe tomorrow

It's late and I wouldn't even be able to use paper because of the light it'd take

[leaden glade]

sure

it's there in the good books

somewhere

[past jay]

Yeah I'm sure someone's managed to break it down into the most fundamental steps possible

Constructing it all the way from basic principles

Probably an assignment from some sadistic professor

[leaden glade]

the matrices are very simple

😃

it's just a bit strange to think about them in that way

but once you do, it's not too bad

[past jay]

So, is there a generalized method for finding inverses of larger matrices? Besides just, taking the A*A^(-1)=I definition and using that to create systems of equations. Seeing as that'd create the same number of equations as rows in the matrix and you'd basically be right were you started.

I know there's Gauss-Jordan for finding inverses but that's more of a technique than a generalized method

[leaden glade]

well, a common algorithm is gauss jordan, yeah

there's also cofactor expansion

which is more straightforward, but longer to do by hand usually

[past jay]

What would be most likely to be implemented in a computer system?

[leaden glade]

gauss jordan

[past jay]

... how? I thought that took some level of playing around with to get it to work

[leaden glade]

not really, you can describe it algorithmically very precisely

find a row with a nonzero number, use it to eliminate all other numbers from this column, swap this row to the top, go to next column

[past jay]

Hangon, "eliminate all other numbers from this column"?

Shouldn't the goal for any given cycle be to eliminate all other numbers in that row?

[leaden glade]

in that column

and yeah consider
[1 0 0]
[1 1 0]
[1 1 1]

first cycle you pick the top row and use it to eliminate the two 1s below it

then go on to column 2

[past jay]

Ok... so if you ignore all other columns I can agree you could institute an algorithm to make it into

[1 0 0]
[0 1 0]
[0 1 1 ]

And then.. the algorithm would hone in on, in this case, R₂

But, what if instead you had started with the matrix

[1 1 0]
[ 1 1 0]
[ 1 1 1 ]

then after the first "cycle" you'd end up with

[1 1 0]
[0 0 0]
[0 0 1]

Right?

So how would you manage to actually get anywhere from that?

[leaden glade]

then the next column is empty

and the last column analysis will lead to
[1 1 0]
[0 0 1]
[0 0 0]

and that's your reduced matrix

of course this doesn't have an inverse

but that's gauss jordan at work

[past jay]

What do you mean the next column is empty

[leaden glade]

it's all 0s

[past jay]

Are you saying you just never use the same row twice? Because column 2 has a 1 in row 1

[leaden glade]

yeah after you use a row you leave it alone

because you're using its initial number as 1

[past jay]

so.. let me see if I've got this straight,

1. Search column n for a non-zero number in rows >= n. Choose first result.
2. Move the row to row n.
3. Use the chosen row to reduce all other numbers in rows greater than n in the column to 0. Reduce the number in the chosen row and column to 1.
4. Increment n.
5. Repeat until n > matrix dimensions

[leaden glade]

yeah

well, you search for column n in rows starting from n

not previous ones

[past jay]

Good point. Originally I was going to say to just remove the row entirely and store it somewhere but figured could just use a variable

[leaden glade]

also you need to reduce all rows in step 3

not just the greater ones

[past jay]

Then you'd be editing rows that have already been reduced, or "chosen"

[leaden glade]

you have to