#geometry-and-trigonometry

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mossy valve
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i dont understand why theres an arrow

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is J 18 degrees?

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is j also 6x+18 im so confused

upper karma
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@mossy valve the angle J is (6x+18)ยฐ

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and since it's isosceles triangle, then their basis will be equal to each other

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6x+18 = 8x

mossy valve
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that makes sense since both of the other sides are equal

grizzled lantern
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they are equal

silent plank
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where did you get stucj?

grizzled lantern
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AM and MB are equal

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so AM+MB = AB

silent plank
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what exactly were you solving?

grizzled lantern
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Should get 16x+32=x^2+7x+10

chrome crater
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OH YEAH

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BRO

grizzled lantern
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then we subtract the left side and get x^2-9x-22

chrome crater
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thanks

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so smart ๐Ÿ™‚

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i feel dumb

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thank you

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both of you

grizzled lantern
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no problem

magic wasp
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hey guys

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!av

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never mind lmao

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hopin yall are doin good

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peace out

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:P

next jackal
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I didn't understand why we had to take a line which passes through 0,1 and r,0 . Why did we take an X intercept in the first place?

lean citrus
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I didn't understand why we had to take a line which passes through 0,1 and r,0 . Why did we take an X intercept in the first place?
@next jackal I don't understand your question; a straight line with a y intercept of 1 should have a an x-intercept

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Except for the line y=1 which does not intersect the circle at any other point

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If your question is "where did this construction come from" I would recommend you read the whole proof

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The aim is to find a paramteric form of Pythagorean triples

next jackal
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The aim is to find a paramteric form of Pythagorean triples
@lean citrus didn't we already do that by showing (a/c)^2+(b/c)^2=1?

lean citrus
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No see that's not a parametric form

next jackal
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I didn't get what the number r signifies here, is it just an x intercept? or is it like an input for a side of triangle?

lean citrus
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Yes when you construct the line, you consider r to be the x intercept

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Now the goal is to express both x and y in terms of r

next jackal
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why in terms of r?

lean citrus
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Well that's what we are aiming to do!

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Define all possible Pythagorean triples

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What we have done is derived a general form of the Pythagorean triple in terms of a single paramter

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Lemme give you a simple example

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"all odd numbers are of the form 2n+1, where n is an integer"

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So you define all odd numbers in terms of a single parameter n. By considering different values of n we are to get different odd numbers

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In a similar way, the goal here is to get a form for the Pythagorean triple in the form of a single parameter

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x^2 + y^2 = 1 is a bit difficult to work with

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Coz there are 2 variables

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i feel like I'm not being able to clear your doubt

upper karma
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r is a parameter which can take any real value ,

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Put value of r

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You'll find different rational coordinates

lean citrus
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Yeah I wanted to get that through to researcher

upper karma
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I understood that, It was meant for researcher haha

lean citrus
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I think I'm not very good at explaining things

next jackal
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I want to know how we're taking more than the radius of the unit circle

hollow raven
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What is the problem?

next jackal
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like any rational number, more than unit circle, how're we getting a solution for a pythagorean triple?

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I'll try to go through the whole proof again

lean citrus
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I'll try to go through the whole proof again
@next jackal good idea

upper karma
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I mean. When you square and add those coordinates in terms of r, you get 1

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no value of x and y will be >1 for any r

next jackal
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it just looks like as r increases, value of y intercepting the circle increases too, but doesn't cross 1, if you take from 1,0 .

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how do both increasing values add to 1?

lean citrus
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X decreases as r increases

next jackal
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what? x is r right?

lean citrus
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No?

upper karma
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no

lean citrus
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See see see see see

upper karma
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x is (2r)/(r^2 +1)

lean citrus
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r is a term we have assumed so that we can express both x and y in terms of r

next jackal
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but we take x as r in the point r,0?

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r is a term we have assumed so that we can express both x and y in terms of r
@lean citrus ohhhh

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but....

upper karma
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you derive them in those terms

lean citrus
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but we take x as r in the point r,0?
@next jackal no... That point is not in question... We are concerned about the point of intersection of the circle, and the line between 0,1 and r,0

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This particular construction allows us to express both x and y in terms of a single r

next jackal
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ohh okay

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umm......

upper karma
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x= 2r/(r^2+1) , y= (r^2 -1)/(r^2+1) are coordinates of a point on circle, just expressed in terms of r

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To repeat what Ragnarok said

next jackal
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okayy

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thanks

upper karma
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PROVE: $\frac{\left(tanx+secx-1\right)}{tanx-secx+1}=\frac{\left(sinx+1\right)}{cosx}$

somber coyoteBOT
upper karma
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could somebody help me with this?

silent plank
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what have you tried

lean citrus
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could somebody help me with this?
@upper karma do you need a solution or a hint?

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I like to prove such identities by simply taking the expression on the right, and multiplying and dividing it to the expression on the left

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It's a bad method, but usually works

upper karma
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I did a little bit, wait a min. I'll send you

hollow raven
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Yeah see whats on the right, and try to make it fit the left side, even if it doesnt look conventional

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thats what i personally do too

silent plank
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you can use that idea like this:

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LHS $= \underbrace{\frac{\tan(x)+\sec(x)-1}{\tan(x)-\sec(x)+1} \cdot \frac{\cos(x)}{\sin(x)+1}}_{\text{problem reduces to showin that this is 1}} \cdot \frac{\sin(x)+1}{\cos(x)}$

somber coyoteBOT
silent plank
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which would be considered more acceptable than mixing the two sides directly

lean citrus
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Thanks @silent plank for translating t through Texit

upper karma
lean citrus
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I mean, it's a good idea to break down stuff into sin and cos

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Not much helpful here tho

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At least I can't intuitively rearrange this into the expression required

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@silent plank mentioned this method

upper karma
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ohh i am getting it. Thank you

lean citrus
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I'm sorry my handwriting is extremely bad

hollow raven
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@lean citrus 1000000 times better than mine

lean citrus
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๐Ÿ˜…

hollow raven
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do you write in one flow?

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like it seems like cursive without the joining lines

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its really neat

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meanwhile my sin looks like sn^2 x when i write it

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cause i write it so quickly and mercilessly ๐Ÿ˜…

lean citrus
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lol

next jackal
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I found my mistake. @lean citrus I was assuming all the points on a unit circle were rational coordinates.

dark sparrow
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(1/sqrt(2), 1/sqrt(2)) would like to have a word with you

next jackal
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yes I did something similar to contradict myself

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but thanks

lean citrus
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I found my mistake. @lean citrus I was assuming all the points on a unit circle were rational coordinates.
@next jackal lol

next jackal
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yeah that's why I didn't get why we were doing this derivation

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So if one coordinate is rational, does it mean the other has to be rational too?

dark sparrow
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on the unit circle? no

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counterexample: (1/2, sqrt(3)/2)

next jackal
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okay thanks... I couldn't find one. BTW why does this book say something that seems like it's saying that?

dark sparrow
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does it?

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the book simply says the construction starts with one rational point and generates more points which are distinct from the first but are still rational

next jackal
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okayy....

dark sparrow
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it does not say that a point on the unit circle with one rational coordinate automatically has the other coordinate also rational.

upper karma
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'Many more', not 'only'

next jackal
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okay got it

next jackal
dark sparrow
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$\frac{2r}{r^2 + 1} = \frac{2}{r + \frac{1}{r}}$

somber coyoteBOT
dark sparrow
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as r goes to positive or negative infinity, the denominator does the same

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and $\frac{r^2 - 1}{r^2 + 1} = \frac{1 - \frac{1}{r^2}}{1 + \frac{1}{r^2}}$, so as $r$ grows large $\frac{1}{r^2}$ approaches 0 and so that fraction approaches 1

somber coyoteBOT
next jackal
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Makes sense

upper karma
upper karma
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thanks man

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wait a second...

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He mentioned "Angle-Angle-Angle theorem"

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but that is technically impossible

next jackal
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??????

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what's impossible in that?

upper karma
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i mean an angle does not change if you increase the side length

next jackal
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length of all the sides. not just one.

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So both those triangles in the corner are similar.

upper karma
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oh

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yeah

next jackal
upper karma
lean citrus
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lol we have 3b1b emotes?

lunar sand
untold coyote
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I need help with easy math guys

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what is the mapping rule

tardy fulcrum
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guys i need help

chrome crater
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ok

tardy fulcrum
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with geometry

chrome crater
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alright

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ok then

tardy fulcrum
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ok well then can someone else help ๐Ÿ’€

novel ginkgo
grizzled lantern
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oh boy

upper karma
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Can anyone help me with these two problems, I've been sick for a week and I have no idea what I'm doing.

dire wasp
upper karma
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confused on 18 and 20

silent plank
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what are you confused about?

upper karma
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Hi, if I have a point O on acute triangle ABC, such that angles OAB = BCO and ABO = OCA how can I prove that line AO is normal to BC?

glass rover
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yo can someone help me out with this one

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what is the smallest positive integer value of k such that sin(theta) is negative. (theta is 56 degrees)

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@silent plank if you understand

grizzled lantern
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@upper karma Gotta know your angle theorems

upper karma
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i figured it out

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thanks anyway

grizzled lantern
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gj

upper karma
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ty

glass rover
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it would be a linear pair right

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like 110 for the first one

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70 = 2y

grizzled lantern
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i think its 2y+70 = 180 @glass rover

glass rover
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or 110 = 180-2y

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would be the same answer either way no?

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oh wait no

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70=180-2y

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i took this math a year ago u got me confused lmao

grizzled lantern
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wdym?

glass rover
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since its a linear pair it would be 110+2y = 180

grizzled lantern
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its a supplementary angle so two angles = 180

glass rover
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oh thats what i meant

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but wouldnt 70=2y since opposite angles?

grizzled lantern
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I think you are right

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I was just going off internal angles and angles whos vertices touch

glass rover
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yeah im confusing mysekf

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have fun with geometry...

upper karma
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@upper karma by normal do you mean perpendicular

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ye

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well i'm not sure how you can prove this but.
triangle ABO is equal to triangle ACO

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How so?

pseudo pumice
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anyone able to help me essentially walk me through this college trig course? or have the time to do so? Looking for like tutoring kind of thing idk how that works or if it is allowed etc. very behind, have no clue what's going on....class is online...sigh

upper karma
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you need help with sin, cos, tan?

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@upper karma I'm considering that the statement doesn't necessarily need to be true

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oh yea and wuf idk how to prove it, i just maed a triagnle with those angles specified

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Because I was playing around and I got that angles between AO and BC (k and k') are in this relation: k - k' = a2 - b2, where a2 = BAC - BAO and b2 = angle ABC - angle OBA

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So they are perpendicular if a2 = b2

pseudo pumice
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That's part of it I'm not too sure where that stops and if I get into something different but for the most part I'm seeing a lot of that

balmy egret
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Can anyone help me with reasoning

upper karma
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@upper karma solved it

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Just have to do bunch of similarity stuff

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Then prove a2 = b2

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And from there prove k = k'

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And btw ACO and BCO are not similar unfortunately

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cuz a1 != a2

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but AB'O and BOA' are

surreal vector
umbral snow
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y is easy to find, then x is a cosine law away

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Wait, but that bottom triangle is impossible haha

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@surreal vector

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Yeah both those triangles can't happen

surreal vector
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oh my bad

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I tried to solve it using cosine and sin

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but I got that x is shorter than 30 which shouldnt be possible

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why cant they happen tho?

umbral snow
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The bottom one is a 45 degree angle, which means both sides should be the same

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Similar logic on top @surreal vector

surreal vector
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The bottom one? where do we have a 45 degrees angle here?

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oh isnt the left side is just 25 - 13?

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which leaves me with x = 32.310

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x^2 = 12^2 + 30^2

astral maple
tardy fulcrum
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anyone ?

novel berry
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what is the issue?

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Do you see any nice property of the triangle?

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@tardy fulcrum

tardy fulcrum
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nice property? LMAO what is that?

novel berry
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a property is a feature that the triangle would have

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do you know what it is called when a triangle have two sides of the same length?

tardy fulcrum
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isosceles ?

novel berry
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Yes

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What do you know about these triangles?

tardy fulcrum
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sum is always 180ยฐ , has two equal angles , two equal sides obviously

novel berry
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sum is always 180 degres goes for all triangles! This an important part of solving it yes.

tardy fulcrum
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iโ€™m just confused on what iโ€™m supposed to do because we literally just learned this

novel berry
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okay

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so the triangle is isosceles then the two angels at the bottom are the same

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Can you see the image I sent?

tardy fulcrum
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yes

novel berry
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okay so the third unknown angel what must it be?

tardy fulcrum
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well in the notes we took my teacher takes two angles and puts the like equation and equals it to another one and breaks it down to find x- i feel very dumb rn so sorry if iโ€™m confusing -

novel berry
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don't worry it's fine, but I am asking about the top angel, do you know what it is in terms of x?

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looking at the image I sent with the isoscele triangle

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It should be the same as either the bottom left angle or the right angel. Which one of them and why?

tardy fulcrum
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well i thought the left and right angle were equal and the top is different than the other two -

novel berry
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it says that they are different the bottom left is 2x+11 degres and the bottom right is x-2 degrees

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So the angels opposite of the two sides that have the same length are the angels who are equal

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look at the image I sent to confirm that you see this

upper karma
pearl lava
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is the answer 63?

novel berry
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How did you get to this answer?

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@pearl lava

pearl lava
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I used a square. If the sides of the square is 2, the area is 4. If I triple the sides, the area is 36, which is 9 times. Then I tried it with a circle. If the radius is 2, the area is 4pi. If I triple the radius, the area is 36pi

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so I did 9*7

novel berry
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Cool

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So the way I see is in the new figure all lengths are increased by a factor of 3 like you just said

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since area is length squared this factor 3 gets squared

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so 7cm^2 in the first image becomes 7* (3cm)^2=7*9cm^2

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Nice way of trying some shapes you knew ๐Ÿ‘

pearl lava
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thanks

meager pendant
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I need some help with this question

cinder nacelle
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How do I do proofs good

winged vine
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hey

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How do I do proofs good
@cinder nacelle by doing more proofs

upper karma
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$prove:\frac{\left(sin\theta :+cos\theta :+1\right)}{sin\theta :+cos\theta :-1}-:\frac{\left(1+sin\theta :-cos\theta \right)}{1-sin\theta :+cos\theta :}=2\left(1+cosec\theta \right)$

somber coyoteBOT
upper karma
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could somebody help me with this?

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What have you tried

drifting orchid
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and explain pls

loud flare
long shale
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On the triangle ABC, AB=AC. โˆ  BAC = 120ยฐ. Point D lies on BC and point E lies on AC. โˆ  BAD = 80ยฐ and โˆ  ABE = 20ยฐ
Find โˆ  ADE

hidden crescent
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ab = ac therefore angle b is 60 degrees

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note isoscles

long shale
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isnt angle ABC 30?

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since 180 - 120 = 60, 60 * 1/2 = 30

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i got all the angles but BED, ADE, DEC, CDE

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this is what i got so far

hidden crescent
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you can do something with triangle ADC

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to find angle ADC

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should bring you closer to your answer

long shale
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ADC is 110, BEC is 140

upper karma
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How do I perform rigid transformations on a triangle without a coordinate graph? These transformations are translations, rotations, and reflections. I know how they work, but I donโ€™t know how to construct them. These transformations have to be conducted using a straightedge, compass, and protractor.

pearl lava
silent plank
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image is blurry, are both those angles labelled as theta?

pearl lava
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yes

silent plank
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angle bisector theorem

pearl lava
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thanks

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is the answer 6?

silent plank
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yes

upper karma
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I wrote this problem and solved it but if anyone likes, could you plz also solve it so I can see if I did the problem correctly? Thx

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(also I put the problem in this channel since the problem's basically just a ton of applied trig)

ripe osprey
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thonkzoom what's the point of making it three blocks instead of two

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aside from one of the parts

upper karma
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one of the parts

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for tenshun

quiet mason
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@upper karma send your work and people can review

rocky birch
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is there a way to prove that the max value of a*sin(x)+b*cos(x) is sqrt(a^2+b^2) without using calculus?

dark sparrow
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yeah using the pythagorean formula or the R-formula or whatever else it's called nowadays

rocky birch
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hmm, i didn't know about this

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thanks so much!

tacit cedar
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Hi, guys. I have a question. Given the volume of the pyramid is 500cm^3, solve for the height. Based on the formula V = 1/3bh, is this question even solvable or is the answer just h = 1500/b.

upper karma
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Hi guys! Can help me?

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The following figure represents the flat pattern of a solid. The volume of this solid is:

a) 20 (Root of three)
b) 75
c) 50
d) 100
e) 100 (Root of Three)

Sorry if there is something wrong written by google

novel berry
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@upper karma base area times height! Also don't multi post.

upper karma
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Ok! Thank you!

@upper karma base area times height! Also don't multi post.
@novel berry

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Thank you

novel berry
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Do you see the shape it forms?

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if you fold it

dry pulsar
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I have no clue how to start it

dusky surge
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First hint: what do the red lines represent?

dry pulsar
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90 degrees

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@dusky surge

dusky surge
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Second hint: what is the sum of all interior angles of any triangle?

dry pulsar
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180

fast tide
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write it down as an equation = 180

dry pulsar
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I tried but I did something wrong

fast tide
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2x+13+5x+90=180

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2x+13+5x=90

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7x+13=90

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7x=77

hidden crescent
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One angle is a right angle

fast tide
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x=11

hidden crescent
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therefore the other two angles are complementary

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yes thats correct

fast tide
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addition subtraction multiply and divide

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don't get scared by the math

dry pulsar
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Thanks

fast tide
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๐Ÿ‘

odd blade
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Guys if you use the same reflection twice the object will land where it started right

olive portal
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i need to prove this

odd blade
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0_0

olive portal
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i canโ€™t do anything no more

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my head hurts

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this thing haunts mr

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me*

earnest echo
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What is 0 choose n??

olive portal
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combinations

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of n things taken 0 times

earnest echo
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Shouldn't it be n choose 0

olive portal
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oh fuck

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damn

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oh my god

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it is the other way around

odd blade
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Correct me if I am wrong it has 2 eight

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2 right diagonal and horizontal

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@olive portal

olive portal
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i donโ€™t study geometry sry

odd blade
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Ah ok

upper karma
raven heart
agile tinsel
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Hey guys, can anyone help me with a Vector issue, its for a game engine. I want to somehow offset my vector v (indicated on the image), in a way that it's offset to the left and to the right. Kind of like raytracing in 3 directions to check for empty position to move to. But I have no idea how to approach this offset. I have T(x,y) (desired location), vector v and the position P(x,y).

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I'd like to try and get something like this

wise pawn
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are you trying to get it to shoot around that obstacle then?

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do you know the width of the blocking thing or would you have to find that out

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like I'm assuming you're like playing minigolf and you're at P trying to hit your ball into the hole at t, but there's a wall in the way, so you are wanting to shoot as close to the wall as possible to get around it

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is that basically what you're trying to do?

agile tinsel
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Yeah

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I can get the size of the obstacle

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But the thing is, I can offset it to the side of the obstacle, but I have no idea how to prone and see how much should I add to avoid it

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As depending on orientation it can be +-x, +-y

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(these are units so I am implementing avoidance and going around

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)

wise pawn
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I'm not sure I fully understand but

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what you can do is take the difference between a vector pointing to the corner of the obstacle and your position, that gets you a direction vector pointing exactly where you want to shoot

agile tinsel
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But wouldnt that land me exactly at the corner?

wise pawn
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if your gun/ball you're shooting has width, add half the width to the vector at the corner

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maybe add a little extra just in case that exact amount is absolutely too close

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that make sense or should I doodle a little pic to show

agile tinsel
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Literally add? Doesnt it make a difference how the target is orriented?

wise pawn
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yeah, of course

agile tinsel
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How can I take that into account?

wise pawn
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I don't know what that is

agile tinsel
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That's my biggest issue

wise pawn
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well I can't help you with your problem if you don't know your problem

agile tinsel
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What?

wise pawn
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I don't know what you're drawing

agile tinsel
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Oh

wise pawn
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these are just triangles

agile tinsel
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P is the position we're at, O is the obstacle we're trying to avoid, v's are the vectors

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We have a vector pointing at our target behind the obstacle(the middle one) and we have 2 vectors pointing exactly at the corners

wise pawn
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this is how I'm picturing the scenario

agile tinsel
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Yep

wise pawn
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blue vector is pointing to one corner, and orange dot is where you're shooting from

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you need just enough offset to pass, ok cool

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so our problem is now figuring out how to get that green vector and that solves the whole problem?

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just want to make sure we're doing what we want here cause I'm not psychic haha

agile tinsel
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Yeah we're getting the green vector

wise pawn
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ok what do we know about it?

agile tinsel
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We know the pink vector

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the center of the obstacle

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wait

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We can use the center of the obstacle and the corner

wise pawn
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I'd say we don't know the pink vector

agile tinsel
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I mean we don't know it because we don't know which side we're hitting

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thats correct

wise pawn
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we know the length of the green vector though, and we know the green vector and pink vector are perpendicular

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well, let's not care about which side we're hitting

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we can determine that beforehand

agile tinsel
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Alright

wise pawn
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based on where p is relative to the left or right of the center of the obstacle

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maybe we should do that first since it's easier

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and logically happens first too

agile tinsel
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I am following

wise pawn
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so here I've drawn a dark blue line where the projection will end up, which is to the left of the center of the obstacle

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so it would really end up shooting to the left in our case

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actually it should be computed as the center along the light blue vector, not the center of the obstacle, that doesn't matter

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so you tell me, how do you compute something like this?

agile tinsel
#

What exactly are we computing?

#

The dark blue?

wise pawn
#

you're wanting to decide which side to shoot towards

#

and we determine which side to shoot to depending on whether p is to the left or right of the center

#

and we can look at that by checking the projection along the light blue vector relative to the center

agile tinsel
#

Nono, we should shoot towards both sides

#

As another obstacle may be in place there

wise pawn
#

you're shooting towards both sides simultaneously?

agile tinsel
#

Yeah

#

The issue is just the green vector

wise pawn
#

oh ok then

#

I thought you were deciding where to shoot

agile tinsel
#

Sry @wise pawn this is a big complication, I'll try and research more on my own

#

And get some notes ready

#

It's a bother to ask anyone in discord this

#

I'll look at stackoverflow

wise pawn
#

well I'm complicating it because you're not paying me, I'm teaching you for free lol

#

I have the answer

#

I'm just not giving free answers that's all

agile tinsel
#

Yeah that's understandable

pearl lava
obtuse tapir
#

Similiar shape

spiral hawk
#

First, u want to add 60+100+120 together to get 280, then 360-280 to get an angle of 80 for F

pearl lava
#

yes

spiral hawk
#

Then your gonna take the FECG and split it in half from F to C

pearl lava
#

ok

spiral hawk
#

Now u should have two trinagles with the top one u have two known sides and and unknown side

pearl lava
#

yes

spiral hawk
#

Nvm

#

Wait, missread, FECG is just like a shrunk version of ABCD, since the side lengths of BC is double EC, that means u can double the six the same way to get x = 12, 6*2

obtuse tapir
#

Thats what i thought

#

Decided not to say anything

#

To not sound dumb

pearl lava
#

oh ok thanks

paper marlin
#

ABC is a triangle right angled at B.AB=5 and BC=10,what is angle C?

hidden crescent
#

use your trigonometric functions

paper marlin
#

Yes?

hidden crescent
#

we can take the arctan(5/10)

#

to get angle c

paper marlin
#

I did

#

But I still did not get angle C

hidden crescent
#

degree or radians mode

paper marlin
#

Sorry I am new to trignometry

#

Maybe a bit bad as well

#

Could you please show me the solution for this?

hidden crescent
#

ok

#

== atand(5/10)

#

omg I forgot theres no mathbot

upper karma
#

,w

hidden crescent
#

and this is a math server

somber coyoteBOT
#

Please submit a valid query! For example, ,ask differentiate x+y^2 with respect to x.

upper karma
#

Use ,w

hidden crescent
#

can someone help me solve arctan of 5/10

upper karma
#

wtf is atand

hidden crescent
#

in degreess

#

arctan in degress

#

its for Mathbot

#

but I forgot this server doesnt have it

#

i have never use ,w

upper karma
#

Just do the same thing with ,w

hidden crescent
#

,w atand(5/10)

somber coyoteBOT
upper karma
#

If you want an approximation ofc

hidden crescent
#

yes 26 degrees

paper marlin
#

Thank you

humble pulsar
#

what's tand?

umbral snow
#

tan in degrees

#

@humble pulsar

#

As opposed to tan which works in radians

humble pulsar
#

Oh

upper karma
#

draw the height

flat viper
#

My handwriting ๐Ÿ˜ญ

hidden crescent
#

$sinx=\frac{3}{\sqrt{10}}$

somber coyoteBOT
hidden crescent
#

Therefore opposite = 3 and hyp = $\sqrt{10}$

somber coyoteBOT
hidden crescent
#

note these arent exact side lengths, merely ratios

#

therefore adjacent = $\sqrt{ \sqrt{10}^2 - 3^2 }$

somber coyoteBOT
hidden crescent
#

adjacent = $1$

somber coyoteBOT
flat viper
#

Yeah i solved it

#

Second question is hard

hidden crescent
#

image isnt clear enough

flat viper
hidden crescent
#

w, rotate

#

,w rotate

upper karma
#

,rccw

somber coyoteBOT
faint gazelle
upper karma
#

Consider the theorem of the sum of angles on a triangle

faint gazelle
#

alright cool, thanks

#

after looking into it a bit more, i'm still a bit confused

upper karma
#

Alright

#

Where did you got to

#

If you got to anything

#

The key here is to notice how we can relate the angle 145ยฐ to the inside angle in order to apply the theorem mentioned above

faint gazelle
#

yeah, i got to that part

#

C = 35 degrees

#

that's all i really have for now

upper karma
#

Okay so yeah

#

We want to create an eqn to solve for z

#

And we can use

Consider the theorem of the sum of angles on a triangle

faint gazelle
#

angle1 + angle2 + angle3 = 180 degrees

upper karma
#

Yes

faint gazelle
#

i'm still pretty confused, sorry

upper karma
#

We want to apply that idea exactly the same way you'd do with numbers

#

Is the z what confuses you?

faint gazelle
#

yeah pretty much

upper karma
#

Okay how would you apply it with numbers

#

Imagine you have a triangle with 30 60 and 90 degrees

faint gazelle
#

would z equal the 35 degrees?

upper karma
#

,calc 180-45

somber coyoteBOT
#

Result:

135
upper karma
#

Oops

#

Wait

#

,w calc 180-145

#

No it is not 35

faint gazelle
#

i had a feeling

upper karma
#

Okay

#

So we said

#

angle1 + angle2 + angle3 = 180 degrees

#

Yes?

faint gazelle
#

correct

upper karma
#

And we have our triangle, whose angles are 35ยฐ, 2zยฐ and (5z-2)ยฐ

#

Yes?

faint gazelle
#

yes

#

wait

umbral cloud
#

So how can you relate those angles to 180 degrees?

faint gazelle
#

do you mean 35 instead of 145?

upper karma
#

Sid i have the floor please don't interrupt

#

@faint gazelle yes oops

faint gazelle
#

OH

#

i understand now

#

so, 35 + 2z + (5z-2) = 180

upper karma
#

@umbral cloud i believed it is not hard to understand that i'm helping and i don't like getting interrupted

#

so, 35 + 2z + (5z-2) = 180
Yes

faint gazelle
#

okay, thank you

upper karma
#

Yw

faint gazelle
#

got it all figured out, thank you so much for your help bro @upper karma

upper karma
#

Glad to hear!

sharp socket
upper karma
#

Solve for angle C

unborn bison
#

whoops

#

The number of sides of a regular polygon is 18. Find the measures of an interior angle and an exterior angle for each ploygon.

#

i said interior 160 and ext 20

#

potentially

upper karma
#

$180(n-2)/n$

somber coyoteBOT
upper karma
#

n = 18

#

So interior is correct

#

Exterior is 360/18 which is 20

#

Also correct

unborn bison
#

yay

#

how does it prove those two are parallel?

#

if they are the same

#

thanks for the help โค๏ธ

upper karma
#

Well if the angles are equal then they are parallel

unborn bison
#

i mean the lines

#

it says 2 equals 4 proves p and q (transversal above) are parallel

unborn bison
#

any ideas?

silent plank
#

converse of parallel line theorems

unborn bison
#

they didn't put that in the word bank, @silent plank

#

this is all i've got

#

Alternate int, Corresponding, Same Side interior, Alternate Exterior, linear pair, vertical

silent plank
#

can you see that 2 and 4 are alternate int?

unborn bison
#

i thought 4 would be exterior

#

oh wait im dumb

upper karma
pure cape
#

@upper karma what have you tried

rare pollen
#

a car with a mass of 1100 kg is travelling at 100km/h and collides with a tree and stops in 0.5 seconds. Calculate the force exerted by the car on the tree

#

someone do it adlays

proven totem
dark sparrow
#

can you show what rules you have to choose from?

#

this looks like more of an issue with the answer format than with the underlying math

#

also @proven totem please please PLEASE do not post across multiple channels.

proven totem
#

Sorry. My bad, just a newbie

dark sparrow
#

yeah again i'd like to see the list of rules

#

there are a bunch of possible ways to do this, i just need to know what your system calls them

devout harbor
#

I don't think they will reply, I gave them the answer in #calculus which I shouldn't have done

upper karma
dark sparrow
#

the answer to B is something you should know from theory

#

graphically, going between the graphs of f and of f^-1 is reflection along a line that makes 45 degree angles with both axes

raven heart
zenith garnet
#

im not sure how to go about finding this

#

could someone help me?

dark sparrow
#

think about the sum of the interior angles of the triangle, & how they relate to x, y and z

zenith garnet
#

i do know the interior angles should add up to 180

#

180-(x y or z) = its respective interior angle

dark sparrow
#

yup

#

so (180-x) + (180-y) + (180-z) = 180

zenith garnet
#

ohhh ok ok

#

nr sure where to go from there, sorry

dark sparrow
#

rearrange the left hand side

#

540 - (x+y+z) = 180

zenith garnet
#

ahhh oh so u take out the 180*3 and then add 540 to each side

#

tysm that makes sense

slow bluff
#

hi

#

can someone explain to me why this is true

#

Why does AE = EG

#

and GF = FC

#

what property is this

upper karma
#

tangency

#

triangles DAE and DEG are congruent

slow bluff
#

oh can't believe i missed that

hushed spear
#

Year 9 coordinate geometry

lines with the equation 3x + ky = 11 and 5x + y = 8 are perpendicular, find the value of k.
so i have isolated the gradients and i know that -3/k * -5 = -1 (i think)
because they are perpendicular

hollow raven
#

Change from standard into y intercept form and find the value k for the slope in the 1st equation so thats is the negative reciprocal to the slope in the 2nd equation. m_1 => - 1/m_1

#

for example if the first slope was something like k/2 and the second was -1/4, then you know that k/2 = 4 so k = 8.

teal mica
#

Can anyone explain how you determine if a fraction is greater than 2pi?

hollow raven
#

Wdym?

teal mica
#

I thought the answer was just 1/6 and 5/6

#

But 13/6 and 17/6 were also answers

#

But 17pi/6 and 13pi/6 are both greater than 2pi

hollow raven
#

Do they give some sort of explanation on why that is so?

teal mica
#

Its vague

#

I don't understand

hollow raven
#

Oh I see

#

@teal mica the pi in the sin function is not part of theta's value

#

so it seems really confusing at first

teal mica
#

Yeah it's independent from it

hollow raven
#

yeah, so as long as theta is greater than two pi, you can just keep on incrementing 2pi as it results in coterminal angles

#

as for calculating it, I guess you just gotta check if 2pi/theta > 1

teal mica
#

Sorry kinda got lost there

hollow raven
#

no worries

teal mica
#

I substituted pi(theta) with x

#

then solved for theta

#

Which got me theta = x/pi

#

Then solved for sin which I got 1/2

#

Then referenced it to the unit circle which got me the pi/6 and 5pi/6

hollow raven
#

right

teal mica
#

Then I re-subbed my result with x and then solved

#

which got me to regular fractions

#

But i'm unsure how to determine if those fractions are > 2pi

#

Like pi/6 * 1/pi = 1/6, but how should I go about trying to determine if 1/6 is > 2pi

hollow raven
#

Yeah, I can't give you a truly simple way as pi is a tricky number to handle

#

but the best you can do is divide 2pi/theta

#

if its greater than 2pi, then the result would be less than 1

#

or no

#

you can just check if theta/2 < pi

teal mica
#

If I divide 2pi/theta when theta is pi/6 that would get me 12, but not sure what that means too

hollow raven
#

theta would be 1/6

#

so theta/2 = 1/12 < pi

#

same applies for all other theta values

#

lets say i had something like theta = 17/2

#

theta/2 would equal 17/4, which is 4 with a remainder 1 or 4.25

#

Since thats greater than ~ 3.14

#

we know it doesnt satisfy the range

#

Sorry, my wording is sort of confusing

#

But there isn't really a clear cut way to figure out something like that without testing and checking

teal mica
#

Hmm

hollow raven
#

If anyone would like to contribute please do^^^

teal mica
#

Sorry, just trying to digest it

teal mica
#

So to check I just plug it into the calculator

#

And it equals to 1

next jackal
#

there are no fixed points in a translation right?

dark sparrow
#

yes

next jackal
#

thanks

main mortar
upper karma
#

Then what

#

Did you cut off a part of the problem?

main mortar
#

yes lol

next jackal
next jackal
dark sparrow
#

no

#

it's P + r(Q-P)

hybrid pendant
#

Looks complicated

kindred rapids
#

I've tried so many times but I get stuck and i can't prove it...help

earnest echo
#

Show your work

kindred rapids
#

My work..? What do you mean?

earnest echo
#

What have you tried

kindred rapids
#

Okay

#

So I changed tanร˜ to sinร˜/cosร˜...then I expanded the brackets and then I added the fractions since they all had the same denominator....
After I saw there was a quadratic in sin so I factorised and then I changed cos^2 ร˜ to 1 - sin^2 ร˜....then I'm stuck

upper karma
#

,rccw

somber coyoteBOT
earnest echo
#

If you notice\

$\sinยฒ(\theta)-2\sin(\theta)+1=(1-\sin(\theta))ยฒ$

#

Use difference of squares in the denominator

somber coyoteBOT
earnest echo
#

Use difference of squares in the denominator

kindred rapids
#

Okay
It would be (1+sinร˜) (1-sinร˜) ?

#

For the denominator...?

earnest echo
#

Yes

#

Now just simplify

kindred rapids
#

Okay thank you so much....I'll go do that now

#

But guys....
It has to equal - sinร˜- 1 / sin ร˜ + 1 ...like I sent in the picture of the question
But when I simplify...I'm getting 1 - sinร˜ / 1 + sinร˜

earnest echo
#

(1-sin(x))ยฒ=(sin(x)-1)ยฒ

kindred rapids
#

Yes I understand that

#

But the final answer....I'm not getting it

earnest echo
#

Show me just the last step

kindred rapids
#

Did I do that wrong or..?

earnest echo
#

No

#

$(1-\sin(\theta))=-(\sin(\theta)-1)$

somber coyoteBOT
kindred rapids
#

Oh...I see

#

Let me do that again

#

So what will sinร˜ - 1 be equal to..?

earnest echo
#

Huh?

kindred rapids
#

That up there was 1 - sinร˜ = -(sinร˜- 1)
So what is sinร˜ - 1 equal to?

#

The way they taught us to factorise instead of 1 - sinร˜....we would have (sinร˜ - 1) (sinร˜ - 1)

#

Which is what I have in the first pic of work that I sent.....

earnest echo
#

Well you see
When you use difference of squares of you get

1-sinยฒ(โˆ…)=(1-sin(โˆ…))(1+sin(โˆ…))

#

Now to cancel the term in the denominator you have to factor out -1

kindred rapids
#

Factor out -1 from where exactly?

earnest echo
#

From any one of the term in the numerator

kindred rapids
#

I got through

#

Lol I'm sorry to put you through that....
Thank you so much, I'm grateful

earnest echo
#

Yw

kindred rapids
#

:)

upper karma
#

I just need to know what w x and z are

#

Thats all I need help with

#

<@&286206848099549185>

spiral hawk
#

Since the trapizods are similar, z is equal to 80, y = 105

upper karma
#

I see

spiral hawk
#

Then, since one trapizoid is scaled down from the other, u can take (25/10)*7.2=w

upper karma
#

Mmhmm

#

Oh that makes sense now

spiral hawk
#

Then, its the same idea for x, except now u can make and solve an equation

upper karma
#

I get it now

#

Thank you

spiral hawk
#

(10/25)*15=x-2

upper karma
#

Thank you for helping me out with this

teal mica
#

Is anyone able to explain how to solve this by hand? I get how to solve via calculator... cos^-1(-0.123)... but what steps does the calculator perform to come to the solution?

mild cargo
#

Calculator uses Taylor series expansion

cerulean dew
cosmic pebbleBOT
#
Rule 4

If your question has not been answered for a minimum of 15 minutes, you may use the Helpers tag once. Please do not try to bump your question using this ping unnecessarily. Do not abuse this ping. Do not individually ping users with the Helpers tag without their express permission.

upper karma
#

I still need help

#

<@&286206848099549185>

#

Bruh

#

H e l p m e

velvet heart
upper karma
tiny flax
#

Does anyone know how I can do this?

#

I can't prove angle A is congruent to angle C

median gull
silent plank
#

that is the greek letter theta, usually used as a variable for angles

median gull
#

thanks i thought it was beta cause i kept hearing my teacher say it

silent plank
#

beta: $\beta$

somber coyoteBOT
upper karma
#

how is this not -8

#

shid wrong channel

night snow
#

@upper karma
Because you cannot cancel ANYTHING if there is any + or - in the fraction (that are not within brackets)

upper karma
#

@night snow shit thanks so much

analog pebble
#

Does anyone know how I can do this?
@Mahjestic#9700 Since there are two parallel sides, (AB parallel CD, AD parallel BC), it is given that ABCD is a parallelogram. By the properties of a parallelogram, angle A = angle C

#

then itโ€™s just simple from then on

next jackal
next jackal
#

How do I show that $2(pta+qtb) โ‰ฅ0$? Or less than or equal to all the terms left side of it?

somber coyoteBOT
next jackal
#

dead channel

#

ted help me pls

junior light
#

Can't promise to be helpful but I'll try.

#

For starters I don't know shit about parametric form of a line.

#

But nevertheless I guess you can translate an answer in regular form to parametric form?

next jackal
#

yes

junior light
#

So consider that the two lines intersect in two points, (x1,y1) and (x2,y2). Then show that x1=x2 and y1=y2, and hence you prove that the point of intersection, if it exists, must be unique.

next jackal
#

no I got that

junior light
#

Oh, alright. You're asking about that circle problem?

next jackal
#

yes

junior light
#

Have you proven that any line passing through (p,q) must pass through the circle?

next jackal
#

No that's what I'm trying to do

#

I tried to follow that hint

#

I understood that you can make points on line with distance to centre as the radius

junior light
#

I'm seriously oblivious of the parametric form of a line. I'll take a look at it quickly and see if I can add something valuable.

next jackal
#

Okay thanks

junior light
rain vigil
#

Is anyone free to help me here

west basin
#

just post your question someone will answer eventually

rain vigil
#

May i know how do i answer 4(b)

#

Can someone give me a hint

#

;-;

devout harbor
#

@rain vigil use double angle identity for sin and cos

rain vigil
#

Double angle identity? @devout harbor

#

But thats 2sin theta

#

Not sin 2theta

stark mural
strange quartz
#

Hi guys. I have a question in spherical trigonometry. Given two points on earth A(\lambda_A, \phi_A) and B(\lambda_B, \phi_B), and 2 distances a, b. I have to determine all the points X(\lambda_X, \phi_X) on earth such that, the distance between A and X is b and the distance between X and B is a

humble pulsar
#

Given two points on earth $A(\lambda_A, \phi_A)$ and $B(\lambda_B, \phi_B)$, and 2 distances a, b. I have to determine all the points $X(\lambda_X, \phi_X)$ on earth such that, the distance between A and X is b and the distance between X and B is a

somber coyoteBOT
strange quartz
#

thanks @humble pulsar

humble pulsar
#

๐Ÿ‘

devout harbor
#

@rain vigil use it to go from sin(theta) to sin(theta/2)

#

For sin(theta/2), sin(theta) is it's double angle

rain vigil
#

I have figured it out, needa use triangle form on first quadrant

cosmic timber
#

Hello!
Idk if this is the right channel but it has the geometry in the name so yeah, my question is (this might be to easy for you guys but we just got started on geometry last week) how do i draw and label this

upper karma
#

i just finished ch4 test and I am very confused on why one of my questions was wrong

#

my brain is hurting so low iq rn but

#

i said sas

#

because perpendicular form right angles

#

right angles are equal

#

pqr = psr

#

qr = sr is given, and pr = pr because reflexive

#

apparently the answer was not possible

#

i have no idea

#

help

silk patio
inland canyon
#

helppls

#

ik some rules but like i dont think any of them deal with this

#

and i know like all of the angles have to equal up to 360

#

like x would be 7 right ๐Ÿ˜”

#

wait nvm i got it lmao

#

it was like 100 + 100 + 80 + 80 and x was 7

#

14 x 7 + 2

#

look at me doing stuff

indigo chasm
grizzled lantern
#

@indigo chasm mbos look up the equation for the volume of whatever trapezoidal prism that is

hidden crescent
#

the volume of any prism is given by this formula:

#

$area = base_area * height$

#

$area = base_{area} * height$

somber coyoteBOT
novel berry
#

Volume =base_area* height?

sour jacinth
#

Yeah

modern pond
#

May anyone please help me with this homework? Iโ€™ve no idea what to do

woven walrus
#

how would one find z

hollow raven
#

Then simply use trig ratios to solve for z

#

there are other ways to do it too, see if you can find any alternate solutions!

#

@woven walrus

woven walrus
#

ty

#

so 9/2?

hollow raven
#

im not sure, i havent solved it pandaThink

woven walrus
#

well thanks anyways ๐Ÿ‘

hollow raven
#

my pleasure

violet totem
#

No idea what I do for 1.

silent plank
#

your 4th statement isn't given

#

what does: $\overline{BD}$ bisects $\angle ABC$ tell you?

somber coyoteBOT
violet totem
#

Given?

silent plank
#

no idea why you skipped line 1,
that's what's given, but what does it tell you about the angles involved?

hollow tendon
#

geometry is my favorite

hushed spear
#

how

#

hello everybody i need help with bearings

#

i have no idea what is going on

#

9th grade

upper karma
#

Have you sorted the possibility of posting the problem you are stuck with

#

@hushed spear

hushed spear
#

yes

#

well honestly

#

i have no questions

#

but i have this one

#

Alana hiked 10km in the direction N70E. Bree set out from the same point and hiked 24km in the direction 340T.

what is the difference between the two,

what is the true bearing of Alana from Bree,

and how far west of Alana is Bree, correct to the nearest km?

#

@upper karma

upper karma
#

i have no questions
@hushed spear
I am new here, could you elaborate on what 340T is

#

it can easily be solved by resolving them into vectors if T represents a direction

hushed spear
#

340t is true bearing

#

and what is a vector

coral dagger
#

My teacher said that the green line is tangent

#

Iโ€™m not sure why

#

is it because when Sine=1 and cosine = 1

#

1/1 = tangent?

stiff bough
#

<@&286206848099549185>

vapid lodge
#

<@&286206848099549185> Is the slant height of a pyramid the same as the lateral edge height

teal mica
#

@woven walrus Did you get help on your problem?

#

Use the Law of Sines

main pagoda
dark sparrow
#

no

bright hollow
#

anyone know proofs?

upper merlin
#

i cant see what u have to prove

#

what angles are those

#

nvm thats 6 and 2

bright hollow
#

i need to fill in each empty box

upper merlin
#

ah i see

#

ok so i would do

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1 is congruent it 7 (given)

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6 is cong to 7 (vertical are cong)

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1 is cong to 6 (transitive property????????)

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measure of 1=measure of 6 (def of congruent angles)

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measure of 1+measure of 2= 180 (linear pair)

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measure of 6+measure of 2=180 (substitute m<6 for m<1)

bright hollow
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๐Ÿ

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appreciate it

upper merlin
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yeah did u understand all the steps

bright hollow
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yeah

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ik proof i just dk where to put every theorem and things like that

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proofs*

upper merlin
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yeah it can be confusing because there are a lot of ways to prove this

bright hollow
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yeah

upper merlin
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np

bright hollow
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thanks man

glad oak
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<@&286206848099549185>

sharp plume
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What's csc^3x and so on write them out

glad oak
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what should I do after I split up the exponents?

sharp plume
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Show me your work

glad oak
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and then I can get (cot^2x)(1-sinx)
(I don't know if the way I got (1-sinx) is correct I did 1/sinx - sinx/sinx)

sleek beacon
upper karma
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can someone help me with math

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in mathematics voice

tidal ember
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Iโ€™ve been stuck on this question for a little while and I havenโ€™t figured out the steps in doing it, If someone could dm me the steps in how to do it I would appreciate it (weโ€™re only using sine/cosine law and sohcahtoa in this section of my math course)

sullen nimbus
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There's a rectangle that's 4 vertices by 5 vertices and you need to find the amount of rectangles in it someone asked me that and I said 60 but apparently it's wrong

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I don't get how it's not

upper karma
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If someone can help me with geometry and call and talk please dm me

weak gyro
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The base is 30in and the height is 20in

still mica
#

is the term "parent function" referring to what the shape of the function will look like when graphed?

stuck crypt
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is anyone able to help me? ik its probs not that hard but im a bit confused bc im rushing this lesson

stuck crypt
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<@&286206848099549185>

lament shell
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need help

grizzled lantern
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their slopes should be equal in order for them to never intersect

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find the pairs that make cd's slope equal to ab's slope @lament shell

azure reef
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or you can just draw and see

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i mean

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you are not required to make proofs etc

lament shell
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wait so what numbers would i use, just random ones?

grizzled lantern
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Test them

stuck crypt
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can someone help me understand what to do

sullen nimbus
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what pair of angles have to be equal for both triangles to be the same @stuck crypt

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(Shouldn't be too hard as long as you know the AAS rule)

stuck crypt
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yea i figured it out i shouldโ€™ve read more carefully thank you!

oak stag
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Hi hi! So I'm struggling with hyperbolas (I'm only in high school dfhds don't judge me too hard lmao). I don't have a specific question, I'm just finding it hard to understand the concept in general?? If anyone is willing to help, I can send some examples of questions at the level I need to understand?

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(I'm going to be on another tab, so if anyone gets to this can you ping me pretty please <3)

oak stag
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<@&286206848099549185> (I think I'm allowed to ping here? It's been 15 minutes. If I'm not supposed to, my bad bahaha)

next jackal
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@oak stag hey, I just came here for help too now, I'd suggest you to ask in other questions channel with greek letters beside it, because I'm doing that too now. Sorry for guiding you to an inactive channel

oak stag
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Ok, thanks โค๏ธ

bright hollow
next jackal
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@bright hollow please, only call helpers after 15 mins of submitting your question and no one responding. And if this channel seems to be inactive, ask in one of the questions channel

bright hollow
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@next jackal where should i ask then

next jackal
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see the channels under category "math help"?

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ask in any of them which seem to be free

obsidian thicket
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Can I get help with geo