geometry-and-trigonometry

[acoustic notch]

Well, it checks out

[supple onyx]

Nice

[remote bronze]

can someone help me with this

[viscid patio]

Since n intersects j at one single point, n and j are not parallel
j is parallel to k
thus n is non-parallel to k
And based on the fact that : if two coplanar lines are non-parallel, they intersect
...n intersects k

[viscid patio]

Can someone help

[tulip ingot]

wait guys I got it

the line is going downwards right

and the k is below it

so eventually the line will keep going down until it passes the line k

boom

Q.E.D.

[oak citrus]

[obtuse tapir]

a book

[upper karma]

A book indeed

I mean you got like many bloody sources

[storm portal]

the internet - there are great sources on yt, and i'm sure khan academy since people continue to recommend it

[elder sphinx]

How do I solve this

[storm portal]

you have your sides messed up - side opposite 30˚ is x, side opposite 60˚ is x√3, hypotenuse is 2x

[graceful trail]

how can I solve for the period?

[pure cape]

asin(b(x+c)) + d = f(x) is the function of the sine function where 2pi/|b| is the period

[remote bronze]

is this correct?

[silent plank]

yes

[vapid stag]

so trig is kinda like geometry?

[prime linden]

Yes, the trigonometric functions are interesting in that they are first defined not as some algebraic expression but rather as the process of measuring sides of a right triangle and determining their ratio.

[vapid stag]

So I technically didn't need to learn algebra 2 to get into trig

[prime linden]

Well to do the excercises that test your understanding in trig you need algebra

[remote bronze]

i think it is D but i am not too sure

[silent plank]

how are you getting D?

and why aren't you sure?

[remote bronze]

idk

i am getting d because 42+42=84

[silent plank]

what's your reason for adding 42 to 42?

[upper karma]

Spherical and polar, how often?

[remote bronze]

i am suffering someone please help

[upper karma]

what do you need to prove ABCD parallelogram ?

[remote bronze]

that is what it says to do.

[upper karma]

can someone help please

[upper karma]

I don't get this, can someone explain?

[viscid patio]

Just graph the rectangle

First

They are basically asking you to calculate the percentage of the area of the rectangle in the quadrant III

U know just graph

And u ll understand

Try to use the little squares

As a unit area

[upper karma]

@viscid patio

here's what i got

[viscid patio]

25 is the area right?

Now calculate the area of the rectangle that lies in quadrant III

[upper karma]

yeah but...........

i didn't get a rectangle

i got a square

with 5 as length

[viscid patio]

Come on we don't care

A square is a rectangle with equal sides

[upper karma]

@viscid patio I see

so then

What do I have to do for 8

the rectangle in quadrant 3 would be t w o, that's the area, no?

because l is -1 and h is -2

[viscid patio]

Yes

Sl

So*

Let's recap

[upper karma]

now to get percentage

25/2?

wait no

[viscid patio]

Area of the whole square : 25
Area of the rectangle in QIII : 2

[viscid patio]

Close

[upper karma]

2/100 * 25?

[viscid patio]

Close

[upper karma]

aight maybe im just stupid

i forgot how to do that

hm

wait so

25 - 2 first?

[viscid patio]

its a formila i guess

[upper karma]

that's 23

[viscid patio]

No

[upper karma]

wait wait wait wait

2/25?

[viscid patio]

area / total area × 100

[viscid patio]

Yes

*100

To get it in percentage

2/25 ×100 = 8%

[upper karma]

so 8%

[viscid patio]

Yesss

[upper karma]

wait that's it

o

well thank you :D

[viscid patio]

You re welcoome

[viscid patio]

Arccos, arctan and arcsin

Use a calculator

[upper karma]

@viscid patio is it possible to find the sides of a right triangle with only the 3 angles

[humble pulsar]

Yes, simultaneous equations w/ trig

[upper karma]

|

ZOOM

lol

[vapid stag]

what a troll lol

[upper karma]

how to do this?

[low oak]

3x+5x+3x+5x=96

x=6

AB=3x

[scarlet basin]

hey can somone help me out with this?

AB = 7.2 and CD = 14.2, (7.2 + 14.4) / 2 = 10.8

So EF should be 10.8, but it says it's wrong?

<@&286206848099549185> srry idk if im allowed to tag u guys

[alpine cliff]

Plot it

Either on graph paper if you want to or desmos

[scarlet basin]

@alpine cliff i did

[alpine cliff]

What does the midsegment th. State

The mid segment is the average of the two bases

Find the length of the bases

And then their average

Voila you got your length in exact form

[green osprey]

mathamatics

[remote bronze]

is my proof correct?

[open crypt]

Confused on where to start, any help? I usually dont need help but for some reason I cant plot my finger on were to start. I dont need an answer just a correct first step

[open crypt]

<@&286206848099549185>

[abstract prairie]

https://gyazo.com/39936d613fb17a6741ddf002b5b0a52f
Find x to the nearest tenth

can i get help here

[upper karma]

What's 12

why's 12 sitting on the bottom

anyways

[abstract prairie]

not sure tbh

[upper karma]

Use your Trigonometric Ratios

[abstract prairie]

havent learned those

[upper karma]

$x=10\sin\left(36\right)$

[abstract prairie]

sin(30) = x/10

should be like that

yeah

[upper karma]

Yeah your Trigonometric Ratios

you do know them

why'd you tell me you don't know them

[abstract prairie]

i dont

i asked my teacher

just now

[upper karma]

SOHCAHTOA?

[abstract prairie]

what

[upper karma]

SOHCAHTOA is just an abbreviation on how to find the angles

anyways irrelevant

[abstract prairie]

ahh

[somber coyote]

Several people are

[abstract prairie]

should be 5 then

thank you!!!

[upper karma]

yes

and no

@abstract prairie oi

[abstract prairie]

ohh

[upper karma]

come back

[abstract prairie]

oi

im here

[upper karma]

You didn't round it

[abstract prairie]

yeah

i forgot

5.9

@upper karma

correct?

my teach said its wrong

[alpine niche]

Can anyone explain me from where comes that 160?

[tiny kiln]

Can someone help me with geometry please

[azure laurel]

How do I do this I'm so confused

[grizzled lantern]

did mans get banned?

[unique peak]

X = 3 by mid point theorem

Then find the sides by placing the Value of x

[onyx cloud]

what's giving you trouble

[royal crown]

the = too part

[onyx cloud]

you said you know that you have to combine the fractions

so do just that

combine the fractions

[royal crown]

im so lost

[onyx cloud]

with what

[upper karma]

yeah correct

Sorry dad closed the net

i mean it was 12 am

[royal crown]

@onyx cloud

[onyx cloud]

yeah?

you're missing a term in there

[royal crown]

i fix it

@onyx cloud

u see

[onyx cloud]

you didn't simplify it

theres 2 like terms

[royal crown]

what it simplifies too

[onyx cloud]

do you see the 2 like terms?

[royal crown]

no

[onyx cloud]

then look again

there's 2 terms you can add together

[royal crown]

Sum two sin(theta)cos(theta)

then

^2

[onyx cloud]

you just need to add the 2 cos(theta)sin(theta) together like you said

its just 2sin(theta)cos(theta)

[royal crown]

can you transform that for me

[onyx cloud]

i just told you what to do

you almost have the answer, it's just that last step

[royal crown]

?

[onyx cloud]

but you still have the other terms

not just that one

[royal crown]

lost now

ws ispost to delete anything ?

[silent plank]

where did your sin^2 and cos^2 wander off to?

[onyx cloud]

you had $\frac{\sin(\theta)\cos(\theta) + \cos(\theta)\sin(\theta) +\cos^2(\theta)+\sin^2(\theta)}{\cos(\theta)\sin(\theta)}$

[somber coyote]

maximo

[royal crown]

oh so keep that?

[onyx cloud]

which is right

[royal crown]

ahhh

[onyx cloud]

just add the 2 like terms

[silent plank]

there's no reason to erase them from existence

[onyx cloud]

$\frac{[\sin(\theta)\cos(\theta) + \cos(\theta)\sin(\theta)] +\cos^2(\theta)+\sin^2(\theta)}{\cos(\theta)\sin(\theta)}$

[somber coyote]

maximo

[royal crown]

feel like im wrong again?

[onyx cloud]

now add the two terms i put in the brackets

$\frac{[\sin(\theta)\cos(\theta) + \cos(\theta)\sin(\theta)] +\cos^2(\theta)+\sin^2(\theta)}{\cos(\theta)\sin(\theta)}$

[somber coyote]

maximo

[onyx cloud]

what's

$\sin(\theta)\cos(\theta) + \cos(\theta)\sin(\theta)$

?

[somber coyote]

maximo

[royal crown]

i apologize if i am wrong

[onyx cloud]

add them though

don't just put the brackets

$\sin(\theta)\cos(\theta) + \cos(\theta)\sin(\theta) = ?$

[somber coyote]

maximo

[royal crown]

its already in the bracket ? or add it again?

[onyx cloud]

add it

what does it equal to?

[royal crown]

awwww

^2

[onyx cloud]

no

its not squared

[silent plank]

you're overthinking it

[royal crown]

sorry bro if im bothering you i just dont understand

[onyx cloud]

just add them up

what's xy + yx

[royal crown]

2xy

[silent plank]

a^2 + b^2 + ab + ba= ?

[onyx cloud]

yes

[royal crown]

so 2xy my numerator

[onyx cloud]

no

you still have the two squared terms

[royal crown]

.

[onyx cloud]

here

just let x = cos(theta)

and y = sin(theta)

so now we have cos(theta)sin(theta) + sin(theta)cos(theta)

what does that equal to?

if xy + yx = 2xy

[royal crown]

sin 20?

[onyx cloud]

where did you get 20 from

[silent plank]

you're really overthink yhis

a^2 + b^2 + ab + ba =?

you're really overthinking this

no

[vapid stag]

what's a good time to start physics class? After pre-cal?

[pure cape]

how is this relevant on a math server?

and in a channel for questions regarding exercises and problems

[unkempt glen]

yeah a lot of high school physics uses 0 calculus

past that textbooks will explicitly state velocity as the derivative of position

[onyx cloud]

@royal crown

from what we just did

do you see what is between the brackets?

how can you simplify it

[royal crown]

add together

[onyx cloud]

so what will that look like

show me the answer you'll get

[royal crown]

sin^2+cos^2

[onyx cloud]

go back to our dm

what answer did you give me for cos(theta)sin(theta) + cos(theta)sin(theta)?

[onyx cloud]

@royal crown

sin(theta) * cos(theta) + cos(theta) * sin(theta)

we found out thats equal to

2 cos(theta) sin(theta)

[royal crown]

ye

[onyx cloud]

so now substitute that into

[royal crown]

bracket

[onyx cloud]

exactly

[lofty pendant]

Is quadrilateral a geometry topic?

[wintry tundra]

@lofty pendant yes quadrilaterals are geometry

[lofty pendant]

Oh okay good im in the right channel then.

i need help on my homework

Other channels wont help me..

Does anyone know how to solve a kite

[wintry tundra]

solve a kite?

hmm

definition of a kite is top sides are equal bottom sides are equal right?

[crystal quail]

Yall think it's possible to have a quadrilateral with exactly 3 axes of symmetry? I can find examples of 0,1,2,4. Can say with near certainty 4 is max, and now I'm wondering if axes of symmetry come in powers of 2. Thoughts? (strictly speaking in 2D)

[lament cobalt]

i don’t understand anything about the problem

[obtuse tapir]

similiar means having the same angles

[graceful trail]

Which one of them is true?

[pure cape]

What do you mean?

Thats a sentence stating a fact

Are you asking for the name?

[glass pollen]

can someone help me how to answer the missing statements and reasons

[nova ivy]

Inscribed Angle Theorem

the measure of an inscribed angle is half the measure of its intercepted arc.

[crystal quail]

Kites are defined as only having 1 diagonal be an axis of symmetry right? Like a square would not be a special case of a kite?

[silent plank]

no

kites are defined as quadrilaterals with 2 pairs of adjacent congruent sides

squares have that property and would be a special case of a kite

[crystal quail]

that's strange that a square could still be considered a kite with 4 congruent sides by just saying "these 2 are congruent, and so are these other 2"

[silent plank]

why would it be strange?

[crystal quail]

when you say "2 pairs of adjacent congruent sides", in my eyes, I see that as saying the 2 pairs must be distinct from each other, but I can see how it's hard to word it better to specify the same thing

[silent plank]

well the pairs are distinct, but the lengths of each pair don't have to be

if a distinction was intended, it would be explicitly part of the definition

[crystal quail]

Also, since i have you here, still got a question bugging me from last night. Do axes of symmetry only come in powers of 2? For quadrilaterals I was trying to find all possible values for the number of axes of symmetry. I can think of quadrilaterals with 0, 1, 2, and 4, but not 3

is that just a thing that can't happen?

[silent plank]

yeh, doesn't seem 3 is possible

[crystal quail]

Can you think of any shape that has a number of axes of symmetry that's not a power of 2? off the top of my head I can't

maybe a hexagon?

[silent plank]

triangles

[crystal quail]

oh shit

you right

[silent plank]

can have 3

[crystal quail]

damn, there goes my nobel prize 😂

[silent plank]

n-gons can have n

[crystal quail]

wait that's cracked. Is that something you can prove with simple geometric rules (like not using algebra, vectors, or calculating math)? I'm trying to relearn math from the ground up and my geometry book doesn't use any calculations, just axioms and visual proofs

think i might have found a way for it. If all points on the n-gon are spaced out with the same angles from the center each point should have an axis of symmetry. At least for odd n, I think i can figure out even n. Thank you!

[pulsar spoke]

does someone know how to solve this?

[lament cobalt]

Idk,What Im doing wrong

like I did 2x+7/14=x-3/63

And it said the answer was 23/42

But when i type it in it says numerical values only

[silent plank]

incorrect ratios in combination with lack of parentheses

[violet meadow]

would i set them = to one another

or 4x+5x=180?

nvm i got it

[old remnant]

How do I start with this?

right now I'm using the area of pentagon equation where
m+n = 1/4(sqrt(25+10sqrt5))(2)^2

regular?

oh I assumed each side is 2 so the angles must've been the same

aah that makes sense

[shy venture]

Are you familiar with the trig functions sine cosine and tangent?

47 degrees is the angle, 200ft would represent the hypotenuse, and the height of the building would represent the opposite side which you can use x to represent

[pulsar spoke]

yea we use sin

or sine

[shy venture]

Okay

so you would plug the numbers the question gives you which would be sin(47) = x/200, then multiply 200 to both sides to get 200sin(47)=x then type 200sin(45) into a calculator

Now, since the crane is 5 feet above the ground level that the building is at, you would need to add that 5 feet to the answer you get from 200sin(47)

[pulsar spoke]

wait so its 151

[shy venture]

Sorry I made a mistkae

mistake

the angle is 47, not 45 degrees

[shy venture]

yes

[pulsar spoke]

ok thanks

[shy venture]

You're welcome!

[pulsar spoke]

this is my last problem and in all the other problems i had to use soh cah toa but in this one i dont know how to start off

[ionic bluff]

wow

now listen here kid

have you ever heard of a little something called pythagoras' theorem

@pulsar spoke

[pulsar spoke]

3.87

and the sqrt of 15 is 3.87 so thats the answer alright

[silent plank]

why even bother mentioning 3.87

firstly its not exact

and sqrt(15) is right there

[ionic bluff]

you can actually simplify sqrt(15)

15 = 3*5

so you can say it's sqrt3 * sqrt5

pretty cool?

but it's also near a perfect square

4^2 = 16

so you can also write sqrt15 as 2*sqrt(15/4)

[upper karma]

can someone help me with questions 4 and 6?

[upper karma]

@old remnant that's AMC12

f*cking cheater

ban his ass

[rocky rune]

Need help with the 5th one

[old onyx]

Do u know the formula for finding the surface area of a square pyramid

[rocky rune]

yes but a bit confused

[obtuse tapir]

ok

Where are you confused

[old onyx]

If u know the formula then u just have to plug in the values

[obtuse tapir]

You can create it on your own

[carmine sundial]

Quick question, how many tangent lines can be drawn in a concentric circle? Zero, right?

[heavy haven]

how do i figure out if its cos sin or tan?

[static ridge]

soh cah toa

@heavy haven

[foggy talon]

please check the answer

For DB

I’m pretty sure it’s DB

[static ridge]

gonna need more information i think

[foggy talon]

oh right

I forgot sorry

@static ridge I got the more information

[static ridge]

yea 12 is right since a perpendicular bisector cuts a segment into 2 congruent parts

if youre talkking about length

[foggy talon]

and is AG also 12?

[static ridge]

no

[foggy talon]

oh okay thank you @static ridge

[static ridge]

ag is congruent to cg

yea np

[foggy talon]

how do I find CG exactly?

*AG

[static ridge]

ag is congruent to and cg is congruent to bg and bg is 15

thus ag is 15

[foggy talon]

thank you so much @static ridge

[static ridge]

yea no problem

[novel ginkgo]

i dont get how to solve this

if there was a way to prove triangle ABC was congruent to triange ACD then it would be ez

but other than that, idk how to solve this

can anyone help?

[upper karma]

@novel ginkgo

It's easy. First find AC(in terms of AB and BC- already given) which is equal to AE. So Area of ABE is AB+BC+CD+DE+AC, Simplify and get the anser.

[vapid stag]

Is this it?

[hybrid solstice]

coonfused onn how the pro proportion is set up

[umbral fossil]

@hybrid solstice A squared + B squared = C squared

[silent plank]

apply angle bisector theorem

[umbral fossil]

@vapid stag Is that all the info it gives?

[vapid stag]

yessir

[umbral fossil]

I'm tryna remember what I learned lmao

[vapid stag]

LOL

is all good we're on 1.1

[umbral fossil]

Rotation angle is sketched correctly

My teacher wanted me to do sketch PQR aswell, dunno if that wat yours wants

[vapid stag]

PQR? uhh

I don't think the problem asked for that. So I assume no

[green osprey]

all i want to know is what measurment is m

is it km or lm

[high shell]

...it says cm right there.

like, centimeters.

[green osprey]

no

i mean like which side

like km or lm

it just says m

[high shell]

Ah. Usually, the side opposite to some uppercase angle is called by the corresponding lowercase letter.

[silent plank]

by convention lowercase letters are used to denote the sides opposite the capital angle/vertex

[high shell]

So m would be the side opposite to M: KL.

[green osprey]

ok thanks

[upper karma]

You shouldn't assume it's a right angle triangle

And yes what Ramonov said

[umbral fossil]

Like, label it I mean.

[upper karma]

apply angle bisect theorem

[umbral fossil]

K

[signal otter]

Can someone please explain to me how the s value provided corresponds to that point

[upper karma]

11 pi over 3 is equv to 11 * 180 divided by 3

meaning a 180 degree angle

11pi/3 radians = 180 degrees

@signal otter

[signal otter]

Thank you very much

[upper karma]

why is your arrow at 300 degrees?

[signal otter]

Hm?

Because that value of s corresponds to 300 degrees

I just didnt understand how we got there

[olive cove]

Is that a test?

[vapid stag]

multiple choice question huh?

i'm sure he's got it figured out by now or the time has ran out 🙂

[violet meadow]

oops

Two chords can intersect in the exterior of a circle.

true or false

[prime linden]

11pi/3 = 5pi/3 +6pi/3 = 5pi/3 + 2pi

2pi corresponds to a full 360 turn.

[wind plank]

I need help with midpoints, segment adition and construction, and angle bisectors

this has to do with midpoints

[static ridge]

Wouldn’t HJ also be .75

[silent plank]

drawing a diagram usually helps

[blazing pond]

uh no

its homework

and I got 89 ft for the answer

would that be correct @olive cove @vapid stag

[pine oar]

https://i.imgur.com/ciULB0L.png

https://i.imgur.com/uBjt651.png

Would this be the right way to approach this problem?

I drew it out on paper, but phone is dead rn

[main lintel]

@pine oar #old-network you have physics discord

[dry jay]

unless im mistaken x = 42sin90/sin45 no?

[humble pulsar]

why use sine law?

[dry jay]

thats the section were covering for these question but im guessing they just want 45/45/90 rule etc. aka x = 42sqrt2

yup thats what they wanted

got tunnel vision

[upper karma]

Can someone help me with a problem please

[dry jay]

@upper karma

[upper karma]

ok so

im trying to learn how to do this

(Solve for b) a=11m c=15m, i have to do a square + b square + c square

[dry jay]

oh, wasnt the question the image you uploaded asking for the distance?

[upper karma]

no I figured that out

[dry jay]

so im guessing this is a triangle with 15m being the hypotenuse

[upper karma]

Yup

[dry jay]

well we know Pythagorean theorem states that a^2 + b^2 = c^2; therefore, c = sqrt(a^2 + b^2). when youre only missing one side you can do b = sqrt(c^2 - a^2)

[upper karma]

ok so 11^ 2 is 121 and 15^2 is 225

I add those 2 together?

I’m confused sorry

OHHH

I subtract it

[dry jay]

its just some algebra turning a^2 + b^2 = c^2 into b^2 = c^2 - a^2

yup you got it

[upper karma]

AHH thank you!!

@dry jay wait then once I get my answer for c I square root it right

[dry jay]

yup

[upper karma]

okok 👍🏻

[prime ore]

I know that the length of QA=tan, shown in point Q. But doesn't that mean that tan is equal to sin?

Bit confused

[versed river]

about what exactly

[prime ore]

about tan

So we see that the length of QA, is equal to tan

and the fact that the point Q has the coordinates 1 and tan

But they're equal triangles

so does that mean sin and tan are the same? Since tan is the y coordinate of Q and the coordinates of P would be cos, sin?

[versed river]

What triangles are you saying are "equal"?

[prime ore]

ONP and OAQ

I'm confused about the entire section actually, im not sure if I even get the point of this section

Wait so this is how I am interpreting this section,
(1) We have a right angled triangle ONP, we extend the triangle to form a new triangle which meets at point A

thats it

then i get confsued

[versed river]

Well I'd start by correcting the assumption that ONP and OAQ are equal. I'm not quite sure why you think they are. The goal of this passage is just to provide a definition of the tan function, and then to show that this definition is equivalent to tan(x)=sin(x)/cos(x). I can clear up any confusion you have on what a specific part means but I'm not sure I know how to re-explain the entire thing in a different way

[prime ore]

well okay, we know that tan is opposite over hypotheneus, and on the unit circle that relates to sin/cos which. But I don't understand why they have to extend OP to meet the tangent from A

wait nvm 1=cos becauses thats the value/length of x

[prime ore]

But aren't they similar triangles because they have the same angles?

[versed river]

oh you meant they're similar

when you said they were equal?

you should say what you mean

[prime ore]

apologises

Now I'm just confused about the red part where its labelled tan, if they are similar triangles. How can the length of QA be tan and the length of PN be equal to sin when they are the similar triangles?

That makes absolutely no sense to me

Algebraically, it makes sense because you can show it but visually I don't get it

[versed river]

What makes it feel off to you? Those functions are basically defined as the lengths of those lines

[prime ore]

I just said, the length of PN is sin and QA is tan, if PN=AQ how can sin=tan??

[signal swallow]

PN does not equal AQ

[versed river]

the only case where PN=AQ is when theta=0

[signal swallow]

?

[prime ore]

o

so the extension of [OP] is just to confirm that tan=sin/cos?

[tired knoll]

can someone help me explain/prove this, Ive got little clue

<@&286206848099549185>

[tired knoll]

nvm I got it after intense staring

[tiny snow]

Given that everything is as it looks, if it looks like a tangent it is a tangent, what can be said about the relationship between the two areas in gray, defined by ABFG?

You can fiddle with the setup here: https://www.geogebra.org/classic/d7z8ngfz (point B can be moved)

[dense island]

hi can anyone pls help me with this qn?

part (ii)

[upper karma]

https://gyazo.com/fb47cc2c6fd430d98b7209176b933dbe

[upper karma]

if anyone is familiar with Apollonian conics

do his conjugate diameters have to be perpendicular to each other outside of the circle?

[onyx yew]

im trying to prove (not for homework) that there are no five unique points that lie on an ellipse perpendicular to the xy axis such that each group of four points lies on a unique ellipse perpendicular to the xy axis

ive been working on it for the past few weeks and ive gotten stuck

i was thinking for one of the eliipses it can be a circle of radius 1 centered at the origin

since if one of them isnt an circle with radius 1 centered at the origin, it can be transformed to one with a linear transformation

(for context this is part of undergrad research on vc-dimension)

(https://mathworld.wolfram.com/Vapnik-ChervonenkisDimension.html)

trying to prove that the vc dimension of ellipses perpendicular to the x,y axes is less than 5, already proven that its greater than or equal to 4

im fine if i have to get into analysis or other higher level math to do it

doesnt have to be done w/ high school level math, this just seemed the most appropriate category

[wise hornet]

perpendicular to the xy-axis?

[onyx yew]

sorry

meant x axis

or y axis

either works

[onyx yew]

the major and minor axes of the ellipse are perpendicular each to either the x or y axes of the plane

heres an email where i typed it up better

(sadly had to use outlook equation editor tho)

[upper karma]

anyone willing to help me

How to find the distance between the points

[humble pulsar]

distance formula

[upper karma]

Got it. Thanks

[night basin]

Given triangle ABC, the angle bisector of angle B passes through the circumcenter of triangle ABC. Prove that AB = BC.

i understand that it must be an isosceles triangle but not the exact terms?

[agile kestrel]

I got some double square route things

Not for homework

It's a fun challenge

[humble pulsar]

which question specifically?

[agile kestrel]

b

[humble pulsar]

ok one sec

ok what nested radical did you get?

[upper karma]

Fun

[boreal adder]

how can u evaluate cos(arcsin(3x)) in radians
the teacher told us to draw a right traignle but idk how that helps

[agile kestrel]

sorry I didn't know you responded I got √(44 + 4√10)

[humble pulsar]

Arcsin(3x)=y means sin(y)=3x/1

[warm sphinx]

Can anyone help me out today, I am struggling in College trig and need someone to explain more than 1 problem for me

🙏

I ask because im not a math major and I really need this A in the class for my GPA. I wont be using this class for my degree so I legit could use the help.

[livid moss]

Well...

Are you going to say what you need help with?

[humble pulsar]

the answer to your well worded question is 7

[neon hamlet]

How would you classify this?

[silent plank]

in that context your options for sides would be:
scalene, isosceles, equilateral
options for angles would be
acute, right, obtuse

[warm sphinx]

Its a lot more than just a few topics xD so it would take time. and a lot of screenshots.

[neon hamlet]

Ah

[humble pulsar]

yeah well you still havent posted a question.. so idk how much help you're gonna get

[neon hamlet]

so sides would be scalene

[humble pulsar]

yes space

[neon hamlet]

but how would you find out the angles?

[silent plank]

compare it to pythagoras

[neon hamlet]

7^2 + 12^2 = 10^2 ?

[silent plank]

not quite like that

your shorter sides are 7 and 10

determine whether
7^2 + 10^2 or 12^2 is larger

[neon hamlet]

The left would be

149>144

What does this show exactly?

Its an obtuse triangle?

[warm sphinx]

Im doing things on mymathlab and I got this question on the Unit Circle

[silent plank]

no, it shows actually shows the opposite

[warm sphinx]

Homework section 7.5

[neon hamlet]

ah

so acute

[warm sphinx]

Can someone explain to me what P is and a little bit about the unit circle so I can learn and work towards solving these on my own? ^-^

[silent plank]

P is the name of a point with the indicated coordinates

[humble pulsar]

P is a point on the unit circle, which is a circle centered at origin with radius 1

[warm sphinx]

Ok so given this how would I find this point on the unit circle?

so I can set up the problem?

Im like struggling hard lol

I just failed a test on friday on different topics. and I have another one next friday x.x

[silent plank]

you are literally given the coordinates of it

[warm sphinx]

but 🤔 where are said points?

[humble pulsar]

read the question

it's written out

[warm sphinx]

where on the unit circle can I visualize those points being at...?

[upper karma]

how i do this one i remember this tricks things where u point 50 to NO then something

[humble pulsar]

do you know how to plot points on a plane?

[warm sphinx]

like for example where is -1/2 on the unit circle

[silent plank]

(-1/2, sqrt(3)/2) is the point where the
x-coordinate is -1/2 and
y-coordinate is sqrt(3)/2

the unit circle is just a circle with radius 1 drawn over the xy-plane

[warm sphinx]

like yeah I understand that... I just dont know where sqrt(3)/2 would be on the xy plane.

[humble pulsar]

Ok so you need help plotting points?

[warm sphinx]

Im that badly struggling.

yes first I need help plotting points

[warm sphinx]

wait.

-1/2, is legit (1,2)?

: o

[silent plank]

no

i'm showing a simple example of how to plot points

[warm sphinx]

that would have made a lot of sense.

wait! Rise/Run right?

[silent plank]

the green dot has coordinates (1,2)

[warm sphinx]

or... Run/Rise?

🤔

so 1 would be the Run and 2 would be the rise in 1/2

[silent plank]

this doesn't really have anything to do with that

[warm sphinx]

oh..

[silent plank]

from the image the point (1,2) is at that position because that's where the x-coordinate represented by the first value is 1
and the y-coordinate of the point represented by the second value is 2

[warm sphinx]

Oh ok

so instead I would plot 1/2 at 1/2 = x but whats really bugging me is where do I post sqrt(3)/2

like where is that on the y-axis

do I put it in the calculator, get a decimal and then just plot a guessing point?

like an approx?

[silent plank]

well sqrt(3)/2 is approximately 0.866
you don't need to be exact

[warm sphinx]

Oh ok

[silent plank]

just place it in the general area

[warm sphinx]

I see

so it would be 1/2,.866

for my plot points

its clicking.

I feel stupid but its going...

ok

[silent plank]

no

[warm sphinx]

its not clicking ok.

[silent plank]

firstly its **-**1/2

and label your y-coordinate as sqrt(3)/2

[warm sphinx]

so it would be in Quad. 4

[silent plank]

no

[warm sphinx]

wait no.

Quad. 2

because x is going backwards

and y is going up

right?

[silent plank]

yes

[warm sphinx]

ok

now this corresponds to the real number of t

scratches head

what is t?

[warm sphinx]

OHH

ok

[silent plank]

apply the definitions of trig functions in the unit circle to determine what's being asked

[warm sphinx]

so that angle = t

angle of theta

wait a minute...

does t in this sense = theta..

[silent plank]

t is just a variable

[warm sphinx]

oh ok

[silent plank]

just like theta

they could use theta or another variable like 😄 if they wanted

[warm sphinx]

so how would I go about finding sin, cos, tan and all that?

its ofc an obtuse.

I have the coord.

x^2+y^2=r^2 right?

and then I would get (r,0)?

and sin= b/r?

and cos = a/r

and then boom I have the Opposite, Adj, and Hyp?

and can find out the rest?

@silent plank

[humble pulsar]

Points (x,y) on the unit circle map to equivalent points (cos(t),sin(t))

[warm sphinx]

so what I said was not correct?

so would x = Opp or Adj or Hyp?

and if that is it what would y =?

and then youre looking at a^2 + b^2 = c^2

[meager carbon]

does anyone want to mentor a self taught leanrer?

[warm sphinx]

wait r=1

[neon hamlet]

How would I get the longest side/shortest side here?

[warm sphinx]

can anyone tell me if I got that right? it will let me know if im following the right track

So far I have Opp. = Sqrt (3)/2

Adj. = (-1/2)

and Hyp = 1

but then I need to also remember is Sin is only positive in Quad 1 and 2

Tan in 1 and 3

and Cos in 1 and 4

but the problem with that idea is that I get this

and something doesnt seem right about that

or this

Sin = y/r .. Cos = x/r.. and Tan = y/x

[humble pulsar]

those are right.. just simplify them

[warm sphinx]

ok how so?

@humble pulsar

[humble pulsar]

simplify them like any other stacked fraction

[warm sphinx]

sooo...

: o

LOL im so sorry

I would put them into decimal?

[humble pulsar]

No

how do you divide fractions?

[warm sphinx]

flip the 2nd fraction and cross multiply them?

😮

[hazy wyvern]

Multiply the bottommost part with the topmost (while also removing the bottommost)

It would become -2 in this case

[warm sphinx]

o.o

[hazy wyvern]

Isn't that how you do stacked fractions?

[warm sphinx]

I... think so.

for the first one

I got sqrt(3)

doing that

[hazy wyvern]

Negative

[warm sphinx]

and then I got -2

and oh?

-sqrt(3)?

[hazy wyvern]

Yep

[warm sphinx]

ok

so 3 people and 1000 questions from me later I can now solve Question 1 and 2 of my homework...

man am I in trouble..

and I also need to remember

All Students Take Calculus

Q1 = All positive

Q2 = Sin Positive

Q3 = Tan Positive

[humble pulsar]

yeah we know CAST rule

[warm sphinx]

and Q4 = Cos post

and ye

so if I keep that in mind...

only ones that will be positive with this being in Q2

is Sin

and Csc

right?

[humble pulsar]

yes

[warm sphinx]

if I do Tan I need to put a - in front of it

and if I do Sin I need to remove the -

right?

or

?

[humble pulsar]

You have the minus sign when it's negative

[warm sphinx]

now what if its Sin = - 1/2

[humble pulsar]

that's not a thing

[warm sphinx]

so I go "Nope Not today!"

and go

Sin actually = 1/2

[humble pulsar]

sin = -0.5 isnt a thing

[warm sphinx]

Ik its an example

like if its already neg do I just got

[humble pulsar]

sin isnt a thing in math

[warm sphinx]

"forget that neg"

[humble pulsar]

sin(t) is

[warm sphinx]

ok...

well

Sin(t) = -1/2

would I just be like

no

Sin(t) actually ='s 1/2

?

[humble pulsar]

tbh I have no fucking idea what you're even going on about

[warm sphinx]

ok

im in Q2

right?

so Sin will be positive

[humble pulsar]

sure

[warm sphinx]

lets say if I have the answer Sine(t) = -1/2

right?

Just because its in Q2 do I just throw that - in front of the fraction away?

because Quad 2 rules?

[humble pulsar]

sin(t) = -1/2 in quad 3 or 4

[warm sphinx]

so yes

it will change to positive automatically in 1 or 2?

no questions asked?

😖

[humble pulsar]

Sine is positive in 1 and 2

it doesnt magically change because of the quadrant

[warm sphinx]

So.. leave it as -1/2?

or make it 1/2?

[humble pulsar]

You leave it so that the statement is true

[warm sphinx]

Ahh ok

[humble pulsar]

you dont change it to get rid of the negative sign willy-nilly

[warm sphinx]

I didnt think so but I had to ask..

Alright! Next Question1

a lot simpler..

would -6 be the Amp or the Period?

[humble pulsar]

neither, amplitude and period are positive numbers

[warm sphinx]

so... 6 would be the amp or period?

: o

[humble pulsar]

yes

[warm sphinx]

which one would it be?

[humble pulsar]

you tell me

[warm sphinx]

Uhhh

imma go out on a wim here and say... period?

o.o

Like I said im in a lot of trouble atm xD

[humble pulsar]

No, cause period is something that affects the x values

[warm sphinx]

wait

so

6 = Amp

and 7 = Period?

ok

O.o?

did I get that right?

Im really trying here xD

[humble pulsar]

No, period is $\frac{2\pi}{k}$ if $y=A\sin{[k(x-h)]}+c$

[warm sphinx]

o.o

[somber coyote]

moshill1

[warm sphinx]

I see

so in this..

it would be $\frac{2\pi}{7}$ ?

[somber coyote]

IamKingSage

[warm sphinx]

@humble pulsar

[humble pulsar]

yes

[warm sphinx]

then I need to simplify?

[warm sphinx]

if the amp is 4, the period is pi/3 and the phase shift is -1

how would I plot those points?

because I ge this weird Zig Zag on my calulator...

looks almost like a seismograph reading lol

[humble pulsar]

Almost like earthquakes travel as waves. . .

[obtuse tapir]

shit

[vapid stag]

is it useful to memorize prime numbers up to 1000?

[umbral snow]

Ye

[remote nimbus]

Useful for what?

You can always google them.

[placid jasper]

Solving problems.

[livid moss]

It's not useful if you only memorize up to 1000. You need to memorize the first 1000 primes, then the usefulness will become clear

[pastel mirage]

can someone explain me on this circle, where is vercosine, covercosine, and haversine is located at, i see the text in image but dont know on which line they lie

[meager carbon]

I’m about to take a geometry course on YouTube so hyped I’ve taken trig logs exponents now I’m taking geo I’m Freshening up bc I quit college (wpi) after one semester due to personal issue and I have to admit I remmeber a lot and can follow it easily anyone want to join me when I begin a new text book in a few hours of proof and logic by zhang I think transitions to advance mathematics or something

[plain nimbus]

Help anyone?

[silent plank]

outside angles theorem (circle geo)

[plain nimbus]

I study in another language

So this is something completely alien to me

[silent plank]

Google what I mentioned above. you should get nice images.

[plain nimbus]

Mkay

[latent berry]

Hey guys, please solve the qotd in MODS...

[crude yarrow]

help:

[strong socket]

i am in uni and have never heard of covercosine, vercosine and haversine wtf is that

[native snow]

I’m really confused on this question and don’t know how to answer it. If someone could just point me in the right direction that would help a lot.

[humble pulsar]

https://www.youtube.com/watch?v=cf0ibYAJVys

There were lots of trig functions that ended up not getting used

[storm portal]

try clearing complex fractions

[thorny charm]

I have a larger problem I'm working on that I can't express in a concise way but boiling it down to one part that I'm not sure how to do is a question I can ask
Say for example the interior angles of a regular pentagon are 108 degrees
Then of course because of the symmetry rotating the entire pentagon 72 degrees will cause it to line up exactly with itself
On a smaller scale given one of the angles can you calculate that? What is the relationship between the '108' and '72' degrees?

Specifically trying to figure that out for an interior angle of 98.2 degrees
Both of the lines do meet whatever condition will cause them to line up after the rotation
I'm just trying to find which point that's at ^^'

[green osprey]

its late and i might be stupid rn

but like can you figure out the area of a triangle just with a permitted

and if not what angles give you the largest triangle

[upper karma]

Sum of interior and exterior angle will be supplementary (i.e. 180)

[abstract prairie]

https://gyazo.com/ec3835a9e642f1bd088e862cc7e3fc1a

may i have help here

[humble pulsar]

just take inverses of both sides

[abstract prairie]

uhh

what does that mean

[humble pulsar]

do you know what sine inverse is?

$\sin^{-1}$

[somber coyote]

moshill1

[abstract prairie]

i do not

[humble pulsar]

arcsin?

[abstract prairie]

nope

is that even a word

i never heard it before

[humble pulsar]

do you have notes?

[humble pulsar]

it's the american notation for inverse sine

[abstract prairie]

ahhh

hmm

[humble pulsar]

Cause I doubt your teacher taught you trig w/o teaching you the basics of inverse trig

[abstract prairie]

this is trig????

[humble pulsar]

. . .

yes

[abstract prairie]

wtf

im in geometry

[humble pulsar]

sine cosine and tangent are trig ratios

[abstract prairie]

well maybe thats why this dosent make sense

for me

im so confused

[humble pulsar]

$\sin{A} = 0.6 \implies A = \sin^{-1}{(0.6)}$

[somber coyote]

moshill1

[abstract prairie]

hmmm

[humble pulsar]

which is about 36.9 deg

[abstract prairie]

for a?

[humble pulsar]

yes

$A \approx 36.9^{\circ}$

[somber coyote]

moshill1

[abstract prairie]

ahhhh

and b is 5/12

[humble pulsar]

no, cos(B) = 5/12

[abstract prairie]

ohh

this is still very new to me

@humble pulsar do you think you can help me with B and C?

[humble pulsar]

I mean.. talk to your teacher about it tbh

[abstract prairie]

kk, i will

thank you!

[graceful spear]

so when it comes to proofs and geometry is there like a list of axioms we can go off of? Interested in learning about geometry with proof stuff but just wanted a clear basis of what is defined already to work of it.

Along with this things like what defines specific shapes and their interior angles sums.

[green osprey]

@delicate venture

u pog

[storm heath]

Why was it made 9 times instead of 3 times?

[humble pulsar]

(3r)^2

[storm heath]

But why>

[humble pulsar]

cause you tripled the radius

[storm heath]

Oh.

Okay.

[white vapor]

how would you find the area of a right triangle with only knowing the two legs are 1.8 and 3.2?

[prime linden]

Pythagoras theorem?

[white vapor]

how would i use it

ohh i thought the hypotenuse was the other leg

i see now thx haha

[upper karma]

Hello can someone help me in #help-0

[silent plank]

why would you even need pythag?
A = bh/2

[upper karma]

command how

,\frac

\frac{1}{2}

whattt

,heh,

,\frac{2}{2},

EH

put $ around the tex.

And #bots for this.

$\swrt$

[somber coyote]

Skyler
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[upper karma]

))

)_)

[green osprey]

I'm solving a triangle and all i have is the angles, its a right triangle but would i still use law of cosine?

wait

you cant do that

my bad

[humble pulsar]

You can use sine law and cosine law on any triangle

right triangles just dont need them

[upper karma]

I need a small bit of help.

Thales theorem.

I know this is the way.

And I know I can do 2a/b = 8/x and 2/b/a = 8/x

That means 2a = 2b = 8 and a = b = x?

Or my reasoning is wrong?

[pure cape]

Yes

Your second equation is wrong, or maybe you are just trying to bring the a down in the denominator, but that does not implies 2a=2b=8 and a=b=x

And you should find a and b first

Notice AGHB is a parallelogram