geometry-and-trigonometry

[upper karma]

Are these w different symbols?..

,rotate

[upper karma]

I'm referring to number 2...

[primal jasper]

Neat! I’m also going to be trying to myself out of precalc to go straight into BC calc when I get back from Germany. I’ll look and try and find some good ones for you!

[primal jasper]

They’re both arcs

[upper karma]

Well I must go find videos online about chords because this packet just sends problems at me

[primal jasper]

Organic chem tutor has some good videos

[upper karma]

So far none of them explain a problem like or similar to mine

[upper karma]

Gen tweakin

😭

I think I got it :D

[sturdy dirge]

ok so the formula is y= A cos (Bx-c)+D. im missing B and im not sure if theres a C value?

so one period goes to 2pi/3. but idk what to do with that ooooff

its so hard to get past a hurdle when i dont know what it is im not understanding

[upper karma]

Would this be a valid way to solve it

Oh my God nvm

I keep solv8ng for the wrong darn thing

[rugged shuttle]

There’s not much to algebra beyond like rational functions and logarithms

If ur a senior in high school, maybe try reaching out to some math professors and doing research on algebra

[maiden brook]

not true bruh

in fact rational functions and logs are probably two of the easier units in algebra

[sturdy dirge]

truth

i think my brain is mush fr fr

[blazing veldt]

Try finding the amplitude, period, phase shift, and midline.

[sturdy dirge]

im having a hard time understanding what to do with a period. i know a period equals 2pi/b. and on this graph one period is 4 right? so would i do 2pi/b = 4 and solve for b?

i did it 😄

[maiden brook]

stuff with inequalities can get very hard

and theres obviously much more than that

[maiden brook]

just transformations of functions

[sturdy dirge]

its difficult for me is all but i figured it out

[maiden brook]

ok good

yeah I see it’s an unconventional function

[rugged shuttle]

Like what

Like as an actual question not trying to be rude

I’m curious

[clear anvil]

A corollary of the Pythagorean theorem's converse is a simple means of determining whether a triangle is right, obtuse, or acute,

Obviously i know how to show this, but my actual question is

why is it called "pythagorean theorem's converse"

[dark sparrow]

pythagoras is "right triangle => a^2 + b^2 = c^2"

its converse is "a^2 + b^2 = c^2 => right triangle"

(suppressing details™️)

[clear anvil]

correct

so like how does that relate to the triangle being acute/obtuse

well a^2 + b^2 > c^2 -> acute

and the reverse for the obtuse case

sorry if i'm missing definitions

but how does a^2 + b^2 = c^2 -> right triangle talk about acute/obtuse case

(i'm more concerned about the definitions of maybe corollary and the converse and how that relates than the actual theorem)

[dark sparrow]

it does not

[clear anvil]

hmm okay so uhhh how do they use that green sentence to introduce the red thing

[dark sparrow]

are you concerned about understanding why the red stuff is true or the formal logical linking in this paragraph

[clear anvil]

😭 maybe both? unless you're busy to explain both

[dark sparrow]

idk like

the formal logic seems a little bit shoddy here

as for why the red stuff is true idk like

do you know the law of cosines

[clear anvil]

😭 yes i'm aware how to derive it with law of cosines

sorry i didn't see your message

you can ping me

i guess i was concerned about how they link stuffs

because i wanted to "parse this information" for someone who isn't familiar with law of cosines and the like

[merry mulch]

A rectangular sheet of paper 30cm*60cm can be formed two right circular cylinders in two ways, thus the ratio of volumes between the cylinders equals to:

[dark sparrow]

!status

[lime crown]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[dark sparrow]

@merry mulch

[merry mulch]

4

[dark sparrow]

you could have posted your work and answer

[merry mulch]

I think the ratio should be 1:1

[dark sparrow]

ok show how you got that

[merry mulch]

as the volume shouldn't be different since both would occupy same amount of space

[dark sparrow]

that's your entire reasoning?

how do you know they occupy the same amount of space?

[merry mulch]

as they are formed from the same rectangular sheet

[dark sparrow]

their lateral surface areas would be the same maybe, bc you're folding the same sheet up. but this doesn't by itself imply their volumes are also the same!

ok so to not run around the bush, you are wrong.

[merry mulch]

does volume differ even though it's from the same sheet? How's that possible

[dark sparrow]

do you want to be taken through how to work out the 2 different volumes? yes/no

if you say yes i will need you to NOT JUMP AHEAD

[merry mulch]

yes

[dark sparrow]

do you understand that you are now not supposed to jump ahead of my explanation?

[merry mulch]

remain silent?

[dark sparrow]

no, i didn't say to remain silent.

im gonna take you through the reasoning, and you should work things out, but you should do only what i tell you to do.

understood?

[merry mulch]

ok. got it

[dark sparrow]

alright.

so this is gonna be cleaner to do if we make variables for the dimensions of our original sheet of paper. that way there's less numbers to worry about.

wait actually no, before this:

do you know how to find the volume of a cylinder in general? yes/no

[merry mulch]

yes

[dark sparrow]

ok, tell me the formula.

[merry mulch]

pier^2h

[dark sparrow]

pi, not pie.

and put spaces around your asterisks so they don't get eaten as italics

but ok, great.

so we have this rectangle, whose sides i will call a and b. (for our specific problem, we'll have a=60 and b=30 -- but we will NOT use these numbers until the VERY END)

let us first imagine gluing together the vertical sides of this sheet, so that b becomes the height and the a-sides roll up into circumferences of the bases.

tell me: what will be the radius of the base?

(if you try to tell me the volume at this stage, i will reject it.)

[merry mulch]

a/2

[dark sparrow]

how did you get that?

(i would ask this regardless if you got it right or wrong)

[merry mulch]

radius is the distance form the centre towards circumference and here a is the diameter. so divide it by two

[dark sparrow]

no, a is not the diameter.

so that b becomes the height and the a-sides roll up into circumferences of the bases.

[merry mulch]

b/2

[dark sparrow]

how did you get that?

[merry mulch]

random guess.

[dark sparrow]

bad!!!

i will repeat myself: we're gluing this cylinder vertically, so that:

• b, the height of the rectangle, becomes the height of the cylinder.
• a, the length of the rectangle, becomes the circumference of the base.

i ask you again: what is the radius of the base?

[merry mulch]

by using the formula of curcumference we can get radius

[dark sparrow]

do it.

[merry mulch]

is it a/2* pi

[dark sparrow]

no, it is not $\frac{a}{2} \cdot \pi$.

[somber coyote]

|Ann⟩

[merry mulch]

it's $\frac{a}{2\pi}$

[somber coyote]

Nischal

[dark sparrow]

that's more like it.

note that a/2 *pi can ONLY be read as pi being outside the fraction.

you should have put parentheses, like so: a/(2pi)

understood?

[merry mulch]

yeah. i realized it now.

[dark sparrow]

ok, good.

now

we have the formula for the volume of a cylinder, as written by you earlier: $$V = \pi r^2 h$$ where $r$ is the base radius and $h$ is the height.

for us, the radius is $\frac{a}{2\pi}$ and the height is $b$.

your next instruction is to \textbf{write down the volume of the cylinder in this scenario}. your answer should begin with $V_1 =$ [as after this we will have a $V_2$ for the other scenario.]

{\Huge Leave your expression UNsimplified until I tell you otherwise.}

[somber coyote]

|Ann⟩

[dark sparrow]

write it in latex or on paper.

[merry mulch]

i wanna try latex even though it takes time for me

$V_1=\pi\frac{a^2}{4\pi^2}b$

[somber coyote]

Nischal

[dark sparrow]

ok, not quite the unsimplified version, but this will do.

now simplify this fully.

[upper karma]

π*(a/2π)²b

[merry mulch]

$V_1=\frac{a^2b}{4\pi}$

[dark sparrow]

that is what i wanted to see from nischal, yes. but i will ask you to please not interrupt me here.

[upper karma]

bet

[dark sparrow]

put a space after the pi so that latex does not get confused at the nonexistent command \pia

also check for typos.

[upper karma]

9th grade mathematics

[dark sparrow]

@merry mulch check for typos again, and you messed the latex up.

and you have a typo in addition to messing up the latex.

[somber coyote]

Nischal

[merry mulch]

yeah

[dark sparrow]

ok, good.

so now we have the volume in the first scenario.

[merry mulch]

similarly shall I calculate V2?

[dark sparrow]

let me speak.

the second scenario involves gluing the a-sides together, so that they become the heights, while b rolls up into the base circumference.

you have 2 options:
(1) Do the same song and dance one more time, with all of the tedium involved.
(2) Recognize that the calculation and result will be exactly the same, only with the roles of a and b interchanged -- and from this, write down V_2 directly.

pick one of these two options.

[merry mulch]

2nd one

[dark sparrow]

ok.

write down what V_2 will be.

in the same manner as you wrote down V_1.

[merry mulch]

$V_2=\frac{ab^2}{4\pi}$

[somber coyote]

Nischal

[dark sparrow]

ok. cool.

now write out and simplify fully the ratio $\frac{V_1}{V_2}$.

[somber coyote]

|Ann⟩

[merry mulch]

a/b

[dark sparrow]

how did you get that?

[merry mulch]

by dividing

[dark sparrow]

ok, i guess i can trust you on this one...

since it is algebraic fuckery and you got it right

so now you almost have your answer

for a rectangle of size a by b, the volume ratio is equal to a : b

[merry mulch]

I see. that means the volumes are different.

[dark sparrow]

indeed they are.

do you have anything else to ask about this problem?

[merry mulch]

No. I'm crystal clear now

[upper karma]

it was surface area and volumes? @merry mulch

[merry mulch]

no it was just the ratio of volumes

[upper karma]

Oh

[merry mulch]

My explanation: Since A conatains both scalane and isosceles triangles the right option is d(none)

correct me if I'm wrong.

[faint pasture]

is it bad to look at the options before solving the question and solving it to achieve an answer that equals one of the options this sounds kinda dumb, but hear me out, for eg in this question i was stuck but then i looked at the options and they all contained a^2 + b^2, and ab so i just calculated their values seperately and chose the option that satisfied this probably wasnt the intended way to solve the problem but yea is it not reccommended?

[silent plank]

situational

sometimes the options can provide an indication of what may need to be done
other times, especially with numerical calculations they don't have the same effect

[faint pasture]

yea but like in problems like this one should i avoid doing it this way during practice or is it just fine?

[silent plank]

its fine

doing enough of these, you'll have a better idea of how to do questions
where they ask you to express ____ in terms of a,b,even without options provided

[faint pasture]

i see thank you!

[deft sail]

How do you solve this? I thought it was 14sin45° or 7√2

[dark sparrow]

what's "it"? @deft sail

did you mean you thought a = 14 sin(45°) ?

[deft sail]

I mean that

[dark sparrow]

ok, let's go through this in detail

you know the SOH-CAH-TOA mnemonic, yes?

[deft sail]

Yup

[dark sparrow]

@deft sail still here?

sorry, had to disappear

[deft sail]

Yup

[dark sparrow]

ok

note that a is the hypotenuse here.

so it's sin(45°) = 14/a

not a/14

[deft sail]

Got it

So that means algebraically a√2=28 I think

Then a =(28 √2)/2 ?

[dark sparrow]

overcomplicating imo but yes.

[deft sail]

Makes so much sense. Thank you 🥹

[upper karma]

I feel like the right answer is not here

Question is asking: State if each angle is an inscribed angle, if it is, name the angle and the intercepted arc

Yes I drew on it because the lrining it absolutely fucked

[silent plank]

what do you think the answer should be?

[upper karma]

oph my fuckinjg god i just realized its not an inscribed angle :sob\

its B

[silent plank]

yes

[upper karma]

I was gonna say something like Yes; RQS arc of RS

,rotate

[upper karma]

im not sure whats going on here

also C in the center is not C the line mb

i remarked it as O

anyways

All I know that the Line C is tangent to the Center

which is like Right Angle Tangent

Wait I think if I divide 136/2 I get ? (aka the ans)

[zealous pivot]

Let omega be a circle with center O, A a point outside of omega. Let B, C be points on omega such that AB and AC are tangent to omega. Is there a simple way of proving that A,B,O,C, are cyclic?

So I know that OBA and OCA are right angles, and this should be sufficient

also, I am pretty sure I can do it with coordinates, but I don't want to do that

[tardy vale]

This going to sound dumb, but do circles have vertices? Because ellipses have vertices, and circles are a special type of ellipse, so I'm a little confused if they have no vertices like it was explained in early math classes, or if they do have vertices

[dark sparrow]

circles have only a center

otherwise no point of a circle is distinguished from any other unlike an ellipse's vertices

[tardy vale]

Ok, thanks

[next pumice]

Do centroids always contain bisectors of the sides of the triangle

[mossy garden]

The centroid of a triangle, where its three medians intersect, may not necessarily coincide with the points where the bisectors of its sides intersect, but all three of these points—centroid, incenter, and orthocenter—are collinear, forming the Euler line.

[sturdy dirge]

I'm so burnt out but my trig class ends basically tomorrow

Sobs

And I'm tryna prepare to do well on the final

[trail tendon]

what have you learned

[quick stump]

Idk what an Euler line is but ok

@next pumice is my alt btw

[maiden brook]

here

there are a lot of lines ig but u should be able to find it out

[trim gale]

Guys

Why is Statement 5 reasoned as Theorem 1?

Doesn't make sense

Pls explain

[vocal bison]

Can somebody explain to me why this question is a permutation and not combination? the only thing i can think of is that the pencil and eraser stuff is the “order” but how do i know that for sure?

[maiden brook]

I hate these types of questions because of the ambiguities

but it’s a permutation because the students are assumed to be distinct and so are the objects

so like say there are three of them A, B and C: handing A an eraser would be a different case than handing A a pencil

[iron knot]

Hello iam a student in grade 10
I wanted someone to help me with a math concept
Which why we use tan theta to find slope why we don't use cos or sin
And what is slope by a simple way

Second point what does ax+by+c stands for they tell my in school equation of st line but I don't get it

Third point i solve math problem but i don't understand it's concept well is it normal

[rugged shuttle]

I’m only in grade 9 but I’ll try to answer as best I can

I’m gonna assume we’re talking about polar equations here

[iron knot]

I think a grade 9 here is better than most students in our country 😂

[iron knot]

Thank you ♥️

[rugged shuttle]

I think slope as like y/x and that can change the angle at which a line is positioned

Tan theta = y/x, so if we have y and x we can use inverse tan to find theta and therefore find the slope

[iron knot]

Yes I know but why exactly tan that decide the the slope of line

[random tapir]

dr.hren can give these three things to 3 people if she gives a pencil to A an eraser to B and the coupon to C it would be diffrent than giving a pencil to C etc. thats just my guess im kinda new to the counting principle

[rugged shuttle]

Oh imagine a triangle with y and x as legs and r as radius

The x leg is lined up with the x axis and the right angle is on the x axis and away from the origin

The angle theta the radius makes with the x axis also defines ur slope

[iron knot]

Like a right angled triangle with a base of x axis and y axis is height and hypotenuse (raduis)

[rugged shuttle]

Like imagine this triangle if it was moved left 1 down 1

[iron knot]

Ah ok

[rugged shuttle]

Slope is commonly defined as rise/run or change in y/change in x

And it’s basically how steep ur line is

If we make a triangle around part of ur line we get this diagram

[iron knot]

Ok and why it change in y/x not x/y

[iron knot]

Yes i got the diagram thank you♥️

[rugged shuttle]

Because some mathematician years ago said so

😜

Anyways

[iron knot]

Yes that's right😂

[rugged shuttle]

The steepness of this triangle can either be determined by (change in) y/x OR the angle between the line and the x-axis

Which can also be denoted as theta

[iron knot]

This angle

[rugged shuttle]

Yes 👍

So if we find theta we can then find out how steep the triangle is (and slope)

[iron knot]

What's meaning of how steep

[rugged shuttle]

1 sec

[iron knot]

Take your time bro

[rugged shuttle]

Sorry if this is long I’m still learning a lot of this

[iron knot]

It's alright and thank for caring ♥️ but iam in Arab country so i can face some difficult in English but its alright

[rugged shuttle]

So to find slope we just need to divide y/x

[iron knot]

Ok ok steep is like slope or a definition or denotation of slope

[rugged shuttle]

Mmm… slope is like how steep an angle/line is

[iron knot]

I get it

[rugged shuttle]

I think u don’t really need tan or theta to determine slope, just y and x

[iron knot]

There alot of ways to get slope

[rugged shuttle]

Yeah pretty much if there’s a math problem that u need help on involving this topic then I’d love to help

[iron knot]

♥️♥️♥️Thank you

[rugged shuttle]

For ur question to find slope u only need y and x sin and cos give u either x or y but tan can give u both

[iron knot]

Yes that correct

Ah

1 min

[rugged shuttle]

Second point ax+by+c=0 is “standard form of a linear equation”

We can convert this to slope-intercept form to graph it a lot easier

Which is what people normally use to graph straight lines

(y=mx+b)

[iron knot]

Ok to find that line(slope ) coming from B we use opp/adj is that right

[iron knot]

What every letter stands for

[rugged shuttle]

X and y are coordinates on the graph and a b and c are constant number

Uh my phone is at 2%

I’ll be home in like 30 minutes

Can I finish explaining then or should we chat in dms

[iron knot]

Ok finish it then and have a good day ♥️

Its not necessary we can explain it anytime

[trim gale]

Anyone?

[merry mulch]

base angle of isosceles triangle are equal

that is the the reason for last statement

[merry mulch]

How to do this without calculator?

[grave pond]

Hmm, I'd start by rewriting each term using sin²(x) = (1 - cos(2x))/2, and then hope it ends up telescoping or something.

[merry mulch]

telescoping means?

[grave pond]

Just pretend I said "hope it ends up as something where, for example, a lot of terms cancel out pairwise".

[silent plank]

isn't complementary property + pythag easier?

[grave pond]

I haven't actually done it, so perhaps. Just said what I would be trying first.

... actually, go with Ramonov's suggestion.

[merry mulch]

how?

[silent plank]

do you know the complementary relation between sin and cos

[grave pond]

E.g. sin(85°) = cos(5°), so sin²(85°) = cos²(5°).

[merry mulch]

yeah

sin(90-A)=cosA

[silent plank]

split the sum halfway / loop it around
sin^2(5) + sin^2(10) + ... + sin^2(40)
+sin^2(85) + sin^2(80) + ... +sin^2(50)
+sin^2(45)
+sin^2(90)

and apply the identity to the bolded terms

[merry mulch]

let me try

ohh! I get it so you want to use this $sin^2\theta+cos^2\theta=1$ at last right?

[somber coyote]

Nischal

[silent plank]

yeh.

[merry mulch]

is the ans 9.5?

[silent plank]

yeh

[merry mulch]

thanks. your way was super simple.

[inner vapor]

@inner vapor i’m tagging myself for reminder to try this problem later

[merry mulch]

nice idea

[dark sparrow]

@fast oriole do you know how to use a protractor?

[fast oriole]

dw i got it correct

i was using the wrong numbers

[inner vapor]

what website is that

[obsidian harness]

sin^2 5 + sin^2 85 = 1
......
sin^2 40 + sin^2 50 = 1

So you are left with sin^2 45 and sin^2 90

Ah right already answered lol

[jagged wyvern]

Could someone help? This is physics, but i assumed I was gonna use proportionality, but I got nowhere close to the answer choices

Oh nvm I just had to add the values

My bad

[grave pond]

I think you need to know and use the refractive index of water (which is not something mathematicians go around remembering ...)

[dark sparrow]

isnt it like 4/3 or something

,w water refractive index

[somber coyote]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by ann_dec

[dark sparrow]

yeah

[faint pasture]

@glacial dawn like you know the weirstrass substitutions?
Do those here after subbing in tanx = pi/sqrt(2) it solves pretty nicely after that

[glacial dawn]

no

i know weierstrauss function though

continuous but nondifferentiable

[faint pasture]

Like basically
cos(2x) = (1-tan²x)/(1+tan²x)
And sin(2x) =2tanx/(1+tan²x)

Sub in the value for tan and youll be able to see this format in the final answer

[glacial dawn]

double angle identities?

[faint pasture]

Sure its ugly but the best way to get it done

[faint pasture]

Im not familiar with terminologies sorry

[glacial dawn]

i see

[blazing veldt]

A rectangular sheet of paper measures 12 inches by 9 inches. One corner is folded onto the diagonally opposite corner and the paper is creased. What is the length in inches of the crease?
I have actually tried folding a paper and deduced that the length of the crease is less than 15 inches but greater than 9 inches. But what now?

[ashen bay]

imagine a rectangle

with length 12 and width 9

now ur basically folding the paper in half, right

so it will look like a right triangle

with one side measuring 12 inches and the other side measuring 9 inches

so now ur trying to solve for the hypotenuse

if u know pythagoreans theorem then it should be easy

[grave pond]

Folding along that line is not going to take any corner onto the opposite one.

[ashen bay]

?

[grave pond]

The problem said "One corner is folded onto the diagonally opposite corner".

Your fold will not make any of the corners end up on top of any other corner.

[ashen bay]

um

so i was thinking

the top right corner

onto the bottom left corner

if u fold it like that

then the crease would be like what i drew

unless im wrong

[grave pond]

You're wrong. That would only work if the paper was square to begin with.

[ashen bay]

oh oops

bro im so stupid

this is sad

anyways

um

[grave pond]

If we fold the top right corner onto the bottom left corner, the crease will be the perpendicular bisector of the diagonal between those two corners.

[ashen bay]

oh

ya

that makes sense

[grave pond]

So the crease would be the green line here.

[jagged wyvern]

It's suprising because i manage to used proportionality to find the missing lengths i didnt know the index of water was needed lol

[grave pond]

How sure are you that your answer is correct? In particular, have you taken into account that the ray should bend when it passes into the water, like the drawing clearly shows it doing?

[jagged wyvern]

I know it's strange but here's what I did:

For the 1.7,x,8.1 triangle, I solved for that long side,

8.1^2 - 1.7^2 = 62.72
√62.72 = 7.9

I'm giving 2 triangles, in order to find the length of the light ray (where 8.1 is the hyp, then the shorter hypothenuse for the smaller triangle

3/7.9 = x/8.1
7.9x = 24.3
x= 3.1 (approx)

now to find the length of the light rays I just add it up

8.1 + 3.1 = 11.2m (approximately)

But yeah I couldve done it the usual way with the index of refraction

[grave pond]

3/7.9 = x/8.1
Where on earth does that come from? It looks like you're asserting that C:A = D:B, but there's nothing in the problem description that suggests such a relation would hold.

[jagged wyvern]

😅

I mean it works lol

[jagged wyvern]

Can someone tell me why this is wrong? I know the proportions seem so simple, but I'l be honest i've been stuck with this for months. Could this be a system error, or is it just me?

[ashen bay]

um so triangle ABC is similar to triangle RST right

[jagged wyvern]

I mean angles are all congruent

Am I paranoid

[ashen bay]

ya

[jagged wyvern]

Ye

[ashen bay]

the first option is correct because BC and ST are corresponding sides and AC and RT are corresponding sides

the second option is also correct

[jagged wyvern]

Wait 2nd option?

AB/AC is dividing it's side against it's own side on the triangle

[ashen bay]

because a property of similar triangles is that the ratio of one side to another in the first triangle is always the same as the ratio of the corresponding side to the other corresponding side in the second triangle

srry if it sounds unclear im rlly bad at explaining

[ashen bay]

ya, but RS/RT is dividing the corresponding sides

on the triangle

and since the triangles are similar, the ratios should be equal

[jagged wyvern]

So

All of the options are correct but im trying to find an incorrect proportionality

[ashen bay]

ok um let me check the other options

idk if this is considered telling u the anser

but option 3 is incorrect

do u want me to tell u why

[jagged wyvern]

Ye why not

[ashen bay]

um so AB/RS = RT/AC is incorrect
because side AB is on first triangle but side RT is on second trianble

AB/RS = AC/RT

not RT/AC

the order is important

[jagged wyvern]

Wait give me a second

Ohh

Wow

My mind was playing games on me wow

[jagged wyvern]

Ty I really appreciate it 🙏

[ashen bay]

yw

😁

[ashen bay]

lol it happens to all of us

[bronze oar]

if you ever need help understanding or something you can dm me and i will respond as soon as i can

[uncut grove]

hi guys
hope everything is well
im learning the unit circle
and i think i get how cos is the x
and sin is y i think
i dont get what tan means and how
if any of you feel helpful could you maybe give a short explanation thank you

[hoary totem]

the tangent of an angle is simply defined as sin/cos
the geometric interpreteation is therefore y/x, or the slope of the line

for example, tan(45 deg) = sin(45 deg)/cos(45 deg) = 0.70711/0.70711 = 1
=> a line that forms a 45 degree angle with the x axis has slope 1

its called the tangent because its also the length of this tangent segment of the unit circle

but.. u dont need to know this

[hoary totem]

this is by far the most important interpretation of the tangent

if u understand that the tangent of an angle is the slope of the line it forms, its obvious why the tangent is positive in the red quadrants (I and III) and negative in the blue quadrants (II and IV)

[upper karma]

Tl;Dr
Opposite/Adjacent

I'm not wrong am I

[hoary totem]

he's working with unit circle not triangles

ur not wrong but that only works in acute angles

[upper karma]

Ah

Well then

Tangent line is like idk how to say it but

[hoary totem]

theyre not asking about tangent lines

theyre asking about the tangent of an angle

[upper karma]

Tf they saying abt then 💯

[hoary totem]

the generalized tangent of an angle, that extends beyond 90 degrees, defined on a unit circle

[upper karma]

tan 0 = 0

[upper karma]

Amazing

[hoary totem]

yes tan 0 = 0

[upper karma]

Thanks

Future mathmatician

tan270= not defined

💀

[upper karma]

wtf

[hoary totem]

tan 0 = tan 180 = 0
and
tan 90 = tan 270 = undefined
are easy to understand if u get that the tangent is the slope
a line with angle 0 or 180 degrees forms a flat line, thus slope = 0
a line with angle 90 or 270 degrees forms a vertical line, thus slope = undefined

[upper karma]

Do I need to know the unit circle for geometry

I learn trigonometry in class 8th

If my study guide for the final exam didn't have it

Learnt*

No cap

[upper karma]

Stop fucking lying

istg

[hoary totem]

i also learned it in 8th grade?

[upper karma]

wait I'm talking to koyomi

[hoary totem]

then no

obv

[upper karma]

Wdym then no

Should I be fucking worried if it does have ot

Do u play genshin @hoary totem

[hoary totem]

if it wasnt on ur study guide then u dont have to study for it

[upper karma]

HOPEFULLY

[hoary totem]

ask ur teacher if ur worried

not everyone learns the same thing at the same time

[hoary totem]

no

[upper karma]

become my friend @hoary totem

now

[hoary totem]

uh

no

[upper karma]

Yes

💀

This is one weird away to obtain a friend

Ion think it's working

its racism

Actually

No it's basic rejection

[hoary totem]

guys this is #geometry-and-trigonometry

[upper karma]

European genshin players are clowns

[hoary totem]

take this somewhere else

[upper karma]

Aye it's all u gng not me

what grade are u @hoary totem

[hoary totem]

im neither european nor a genshin player

[upper karma]

Lmaoo I'm out ha e fun wit this shitter

[hoary totem]

im in university

[upper karma]

that's why become my friend

[hoary totem]

no

[upper karma]

can u help me with multivariable calculus

I know single variable calculus pretty basic

which I learnt in class 8th

[uncut grove]

forgive me im a bit dumb why is this the case?

i get what else you said and i thank you for that

[hoary totem]

do u know how to tell if a line is positively sloping or negatively sloping?

[uncut grove]

yes

[hoary totem]

if its going up to the right its positively sloping
if its going up to the left (or down to the right) its negatively sloping

[uncut grove]

ye

[hoary totem]

so all the red lines here are + slope, the blue lines are - slope

[hoary totem]

thus this

the tangent in the red parts are +, the tangent in the blue parts are -

[uncut grove]

so the blue lines is the sin/cos for that quadrant?

[hoary totem]

the blue lines have negative slope, thus the tangents of those angles have negative values

[upper karma]

Damn

[upper karma]

The perpendicular one is sin

And the horizontal one is cos I think

[hoary totem]

more rigorously, consider:
in quadrant I, sine is positive, cosine is positive, thus sin/cos = tangent is positive
in quadrant II, sine is positive, cosine is negative, thus sin/cos = tangent is negative
in quadrant III, sine is negative, cosine is negative, thus sin/cos = tangent is positive
in quadrant IV, sine is negative, cosine is positive, thus sin/cos = tangent is negative

but u dont need to memorize this

[uncut grove]

ahhhhh its clicking into my mind nowww

[hoary totem]

if u know how slopes work then it should come naturally

[uncut grove]

thank you so much brother 🙏🙏🙏

you have no idea how much i needed that

[upper karma]

That's 8th grade geometry bro

[uncut grove]

is it?

[upper karma]

whats ur major? @hoary totem

[hoary totem]

does it matter??

[upper karma]

Yeah

[hoary totem]

if someone is struggling with it then im glad to help

[upper karma]

The first quadrant has both axis positive

[hoary totem]

stop hating for no reason

[hoary totem]

np

[upper karma]

Second one has abcissa negative and ordinate positive

third has both negative

Fourth has abcissa positive and ordinate negative

[upper karma]

when did I hate

Stop assuming bs for no reason

[hoary totem]

stop belittling people

why does it matter if its 8th grade geometry

[upper karma]

The concept is taught in 8th, if you remember the concept, it's pretty simple

[upper karma]

I'm just telling that this concept was taught in class 8th

huh

[merry mulch]

You learnt calculus in 9th?

[hoary totem]

its not unbelievable

the fact that ur bragging about it is cringe tho

[merry mulch]

whose bragging i was just asking?

[hoary totem]

rachit

not u

[upper karma]

8th

Basic of differential calculus

And integral

Expnontial and trigonometric functions

[upper karma]

Tf bro whos talking to u

I suggest you mind your own business

[hoary totem]

says the guy who was begging me to be their friend 5 minutes ago

[upper karma]

You don't know the difference between begging and asking

Get some help 🙏

[hoary totem]

🤔 no i think i know the difference perfectly well

[upper karma]

then apply it

[hoary totem]

only when u stop malding

take this out of #geometry-and-trigonometry anyway

stop ruining math with ur temper

[upper karma]

bet

[merry mulch]

It's not unbelievable but is an achievement to some extent.

[upper karma]

I'm not hro

Bro

You're just taking it to your ego

[uncut grove]

could somebody explain what the reference angle is?

thank you

[merry mulch]

the angle with which you identify base and perpendicular of a right angled triangle

[hoary totem]

in which context?

oh

[uncut grove]

it tells me to find the reference angle (i.e related angle) in the first quadrant

for 227

[hoary totem]

reference angle is the angle expressed as an acute angle

[uncut grove]

227*\

[merry mulch]

send the exact question if possible

[hoary totem]

so 227 degrees

[uncut grove]

ye

how do i find

[hoary totem]

it always helps to draw

this is 227 degrees

[uncut grove]

yes

[hoary totem]

to express this as an acute angle from the x axis (aka "reference angle"), ur looking for this angle:

[uncut grove]

which is 47 degrees correct?

[hoary totem]

yes

[uncut grove]

it says to find in the first quadrant

[hoary totem]

47 degrees is in the 1st quadrant

u can see that any angle between 0 and 90 is in the first quadrant

in general here are the formulae

but u dont need to memorize them

[uncut grove]

ohhhh yeah

[hoary totem]

just draw

ive always hated memorizing formulas, i always solved these kinds of problems by drawing

[uncut grove]

its still prepping me but why is it useful to find the reference angle

[hoary totem]

uhhh

i dont know

sometimes its geometrically useful

like say ur solving for the angles in a triangle

using some formula, like the law of sines

[uncut grove]

ye

[hoary totem]

and u get an angle of 227 degrees on ur calculator after following the formulae

obviously the angle in a triangle cannot be 227 degrees

so u gotta find an equivalent acute angle

which would be 47 degrees

[uncut grove]

ahhhhh ok

this is saying somewhat the same thing you just said?

its the only part i didnt understand

of the page

[hoary totem]

yeah

so

consider these two angles

the red one is obtuse, the blue one is acute

[uncut grove]

yes

[hoary totem]

but theyre symmetric

in fact, they have the same sine value

[uncut grove]

because its mirrored ye?

[hoary totem]

symmetric angles like these often have properties like having the same sine value or cosine value or etc etc

[uncut grove]

ahhh ok

[hoary totem]

for example, sin(227 degree) = -sin(47 degree)

so u dont actually need to find sin 227 degree

just sin 47 degree then put a minus sign in front

this is another reason why reference angles can be useful

[uncut grove]

my friend you helped me understand the whole part

i cant thank you enough

my teacher was talking about this for a whole lesson and i was so worried

i greatly appreciate it 🙏💗

[hoary totem]

np

[formal geyser]

Can anyone find x?

I've been struggling with it

[dark sparrow]

here it is

@formal geyser missing image?

[uncut grove]

no way you found x

[upper karma]

dan

damn

[primal jasper]

Woah! You gotta get this published!

[upper karma]

Anyone?

[formal geyser]

Can anyone find x?

[dark sparrow]

oh that one problem with some kind of weird trick to solve it huh

[silent plank]

adventitious triangle

[formal geyser]

I looked it up on internet

And it's that kind of triangle

But have you figured out how to solve it?

[upper karma]

There u go

Hope this helped ^^

[upper karma]

I thought it was like an isoceles triangle

[formal geyser]

It is

But this problem is also known as langley's adventitious triangle

And currently i am reading the wiki article about it to solve it

[upper karma]

Well I think I may know how to find a few angles that might get closer to solving it

[undone flicker]

its very easy.

[undone flicker]

is it 10 degrees?

[formal geyser]

I dont know

Let's assume it is

How did you do it

If x = 10 degrees, then the triangle doesn't seem to be isoceles

[dark sparrow]

appearances can deceive

who said the diagram was to scale?

[upper karma]

It can't be 10

Well maybe

[upper karma]

Maybe if we get that angle it gets us closer to the solution

[formal geyser]

I already found a lot of angles, but it didnt help. There is another solution

[upper karma]

So that whatever A + the unknown angle of the angle next to A, we get x by misusing it from 180

[formal geyser]

I am reading about it now

[upper karma]

That's based off my geometry knowledge

[silent plank]

basic angle chasing won't help

[formal geyser]

Have you solved it

[silent plank]

can't remember the solution

[normal dragon]

tan opp/adj

the x should be? 41 or -145

[dark sparrow]

how are you getting -145?

[dark sparrow]

but why are you taking 18 radians

when it says very clearly the angle is 18 degrees

[normal dragon]

oops

[dark sparrow]

18 radians is like what, a bit shy of 3 full turns?

[merry mulch]

https://youtu.be/CFhFx4n3aH8?si=QSwfVlqmsqdTtldg

isn't this the exact question??

[formal geyser]

It is

[formal geyser]

Thanks

[merry mulch]

is there a trigonometric way to solve this without those constructions?

[formal geyser]

I dont know

[normal dragon]

tan(18°) = x/128in
x = 41.6
is this correct?

[formal geyser]

think, yes

[merry mulch]

what's x?

is it the height of the tower ?

[normal dragon]

yep

i need to find H

H = x + 80in

h = 4.16 + 80in?

[merry mulch]

isn't h the length of hypotenuse?

[formal geyser]

If so, he needs to use pythagoras

[normal dragon]

i am basing on this btw

[merry mulch]

what's this angle?

[formal geyser]

Or cosine(18°) = adj/hyp

[normal dragon]

18°

[merry mulch]

so what do you need to find the length of?

[normal dragon]

the h

like on the video

[merry mulch]

use cosine trigonometric ratio.

[normal dragon]

we're using clinometer

[normal dragon]

do u have a video of that?

[merry mulch]

wait.

[normal dragon]

i am just base on this vid

btw it is a angle of elevation and depression thingy

[merry mulch]

https://youtu.be/tielQ3ejh70?si=7m566MuB4aKVgsJ7

https://youtu.be/uyKvSe6Ltgs?si=OArdCtrBM5DAZTFe

this one too.

[normal dragon]

H = 4.16 + 80in
H = 84.16

[formal geyser]

A also wanted to ask whether sine law is popular and often used, because i hardly ever see its applications in solving geometry problems

[merry mulch]

h is the hypotenuse of the right-angled triangle. (not the total height of tower)

[normal dragon]

oh

but would it be technically correct?

since i don't know how to solve actually

i only copy the format of the video

[merry mulch]

Did you watch this?

[normal dragon]

wait lemme watch

[normal dragon]

this is the solution i copy btw

[merry mulch]

it's based on this

you need to know this to find any missing sides/ angles in a right angled triangle.

[normal dragon]

most of them are pythagorean theorem

do i need to do that?

or the sohcahtoa

[merry mulch]

do you know it?

[grave pond]

Try all of them and see which one sticks.

[normal dragon]

yeah the soa

cross multiply

[merry mulch]

so find perpendicular (opposite side) in this right angled triangle

[merry mulch]

and add 80

[normal dragon]

H = 4.16 + 80in
H = 84.16

[merry mulch]

no

[normal dragon]

bruv

it's wrong

[merry mulch]

how you got 4.16?

it's not h! the question is to find the total height of that tower. use p instead of h .

[normal dragon]

from the h + x = height

[merry mulch]

can you highlight what h is??

[normal dragon]

i mean

I solve the x

[dark sparrow]

i think that our issue is not with trigonometry as such, but with the fact that it's unclear what the letter x refers to here

[normal dragon]

it's 41.6

[merry mulch]

is this h?

[normal dragon]

yez

[merry mulch]

so how does adding h and 80 give you total height?

[merry mulch]

it's total height

[silent plank]

properties of rectangles and segment addition

[silent plank]

also they've subtracted the wrong way in the image
90°- 72° = 18°

[normal dragon]

look athe vid

[normal dragon]

still 18°

but I'll guess the 90° goes first

[merry mulch]

72-90=-18

if you are taking this part as x

[normal dragon]

integer mb

[merry mulch]

then yeah x=41.6

[silent plank]

you calculated green
from rectangle properties red is also 80
add up lengths of red and green to get the total black length

[normal dragon]

is that still on angle of elevation and depression

[silent plank]

no

its addressing why adding 80 gives total height

[normal dragon]

if i base on this is it incorrect?

[grave pond]

80 inches is 203 cm; is is realistic to assume the kid is that tall? (The number on the picture looks more like 30 but that is on the other hand very short ...)

[normal dragon]

oh yeah he wouldn't be 6 feet 💀

god how do i fix this

so my measurements are the problem after all

bruh

it's confusing me off

should i use meter or inch?

when i measure it

[bleak yoke]

H is greater then 128in at least

[upper karma]

Inches

[somber schooner]

how do we get there

mostly I dont get the 4

from where it came from

[atomic tulip]

sin(2x) = 2sin(x)cos(x)

(sin(2x))^2 = (2sin(x)cos(x))^2

[somber schooner]

I see thank you a lot

[amber hollow]

I'm wondering why im wrong here. my steps in order were:
y = cos(x +3)
y = cos(x+3) +4
y = cos(3x+9) + 4
y = **-**cos(3x+9) + 4

[nocturne remnant]

Vertically compress step should be multiplying rhs by 1/3

(Also, fyi, in the last step don’t forget the minus should apply for both terms)

[grave pond]

And the compress step should only be scaling the x, not the constant you add to it later.

[nocturne remnant]

What are you saying

[amber hollow]

i thought that the form was Acos(B(t-h)) +k meaning the B affects the h when you add it

[amber hollow]

the 4 becomes a minus 4 as well?

[nocturne remnant]

Yeah

But you need to correct the step 3 first

[amber hollow]

i think i misunderstood what you meant by this then

[grave pond]

We already have

y = cos(x+3)+4
For compressing by a factor of 3 we want more wiggles in a given horizontal space, so we need to reach large inputs to the cosine faster. This means that it is correct to replace x by 3x -- but the +3 should stay a +3, so:
y = cos(3x+3)+4
The only thing we do when compressing is modifying the input to the entire computation. The actual computation we do should be the same, including the part of the computation that says "the add three".

Argh -- I misread the task. I've been talking about horizontal compression, but they want vertical compression.

[nocturne remnant]

Does vertically compress not mean squeezing it from the top and bottom

😅

Alright

[grave pond]

Yes, I misread.

[amber hollow]

happens

[grave pond]

So nothing of what has been written is right for vertical compression.

[nocturne remnant]

The inside of cos should still be x+3, I mean multiply the whole thing on the right hand side by 1/3

[amber hollow]

oh B affects horizontal compression

i dont see a single mention of vertical compression in my textbook unless im blind wth

[nocturne remnant]

It should not be difficult to come up with the correct solution if you have a solid understanding of how functions and their graphs are related

[hoary totem]

vertical stretching means u multiply the cosine by a factor

also for vertically flipped id imagine ud also flip the +4 into a -4

[nocturne remnant]

The 4 would be multiplied too, no?

[amber hollow]

I do not ✨. I honestly don't understand much from this book and the only reason I got this far is cause one of ya'll here gave me an impromptu lesson

[hoary totem]

hmm depends on what they want
do they want the whole graph squished or just the cosine

[nocturne remnant]

I think they are applying the transformations one after one

Step by step

[amber hollow]

i understand right triangels and the unit circle now but now they're turning it into graphs and i dont get it

[hoary totem]

i guess this also applies for the flipping

[amber hollow]

isnt that just amplitude?

[nocturne remnant]

Wdym

[amber hollow]

if you multiply the cos/sine by something then that number is the amplittude isnt it

[hoary totem]

yes

stretching/compressing vertically means altering the amplitude

stretching/compressing horizontally means altering the frequency

[nocturne remnant]

This question is testing your understanding of function graphs rather than trigonometry - I could replace cos(x) with just f(x) and ask the same question just as well

[hoary totem]

https://upload.wikimedia.org/wikipedia/commons/0/08/Sine_curve_drawing_animation.gif

its simply "unraveling" the circle

[nocturne remnant]

For your information, if you have a graph whose equation is y=f(x) and you vertically compress the graph by a factor of 3, the equation for the new graph would be y=f(x)/3

If that makes sense

So in your third step, just multiply the entire RHS by 1/3

[hoary totem]

if thats what they want

the question also seems like theyre asking to squish just the cosine by 3

in which case ud only multiply the cosine with 1/3 and leave the vertical shift alone

[nocturne remnant]

I really don’t think so…

Well

It’s an English issue rather than a math one

[amber hollow]

hi sorry my professor found me struggling. apparently the answer for the site is wrong and this should instead be -4 but otherwise yeah i understand compression is amplitude and flipping is making everything negative

[amber hollow]

if you did that i would probably understand it

[hoary totem]

yeah so i was right

its only asking to squish the cosine

[amber hollow]

well it didnt word it properly but yeah

[hoary totem]

yea

[amber hollow]

tysm

[nocturne remnant]

Ok

Damn

[amber hollow]

i think i might watch a video or something i guess. idk why my brain doesnt get this. it was the only topic in calculus that just completely went over my head

[hoary totem]

equivalently, u can think of it as basically

yk how a sine table works

angles on one side, sines on the other

just graphing that table

but understanding the geometrical side is definitely helpful

[amber hollow]

But then why is it sometimes these graphs use integers on the x axis and sometimes they instead use pi

Why is the period sometimes a legit number and sometimes it’s like pi/2

[nocturne remnant]

Are the “legit numbers” in degrees?

[hoary totem]

radians vs degrees

ways of measuring angles

degrees are an arbitrary tradition that comes from ancient babylon

radians are a more.. mathematically natural way of measuring an angle

[amber hollow]

i just mean we go from this

and then now we are this

why

these are degrees?

[hoary totem]

oh, no

this is just

how do i say this

its just different markings

u see how for image 2, the sine graph hits the x axis just after 3

and in image 1, the sine graph hits the x axis at exactly pi

well guess what, pi is just after 3

lol

[amber hollow]

oh

[hoary totem]

in general the pi markings are more useful

[amber hollow]

there needws to be some sort of excercise i can do so that i can actually process pi as a number

[hoary totem]

cuz it shows u exactly where the sine and cosine graphs hit the x axis

[amber hollow]

pi to me looks like a word so i forget its an actual number most of the time

[hoary totem]

just practice will do

lord help me

[frozen ocean]

holy shit

[vernal pilot]

What are you trying to do?

[sturdy dirge]

how can anyone remember all the reciprocal identities of trigonometric expressions

[trail tendon]

... There's 6

[sturdy dirge]

theres more than 6 things to remember

i have 13 written down on a sheet im trying to remember rn

what a yuck attitude to have in a server about learning.

[sturdy dirge]

this is what im referring to theres a lot to keep in mind when working through the problems.

[trail tendon]

Oh you meant more than just reciprocal identities

[trail tendon]

😂 I don't think it was that bad lol

[cunning lion]

many of those can be derived from the others

[sturdy dirge]

im just saying its condescending when i only said that to see if anyone would have tips for me but yep

[cunning lion]

e.g., the second two pythagorean identities come from dividing both sides of the first one by cos^2(theta) and sin^2(theta) respectively

[trail tendon]

I thought u were just complaining 😂

[cunning lion]

as long as you remember the quotient & reciprocal identities (since they define the functions), a bunch of others just come out of it (e.g., the even odd identities for every function other than sin and cos can be found by dividing the appropriate identities involving sin and cos)

[sturdy dirge]

and what was your goal of what you said? it had ill intent behind it and i dont appreciate it. thats all im saying.

[sturdy dirge]

thank you yea i will keep that in mind im just cramming it in bc i have an exam at the end of the week

[trail tendon]

I'm sorry lol I don't mean to disincentivize learning

[empty yew]

Is it really pre-university math?😱😱😱

[hoary totem]

well technically yeah it involves no math above high school level :p

[upper karma]

The great circle

[vernal pilot]

Angle identities are fun. But you really only need to know sin^2(x)+cos^2(x)=1, tan(x)=sin(x)/cos(x), and the reciprocals

[sturdy dirge]

Bet I'll focus on those then
Thank u 🙏

[vernal pilot]

Np

[upper karma]

csc²x-cot²x=1

sec²x-tan²x=1

[boreal marsh]

guys i have a quick question, when do i know pi equals 180 or 3.14 when working with angles/radians

[dark sparrow]

pi, the number, equals approximately 3.14 (sometimes 22/7 is also used as an approximation, but it is an approximation still)

pi radians = 180 degrees is a unit conversion

you would not say 1 = 12 just because 1 foot = 12 inches, would you?

@boreal marsh

[boreal marsh]

true

that makes sense, thank you very much

[boreal marsh]

rlly appreciate your help

[serene tartan]

could anybody hop on a call with me and explain to me these geometry questions, im in online school and i need help

[inner vapor]

why not send the first question here as an image?

maybe someone can help

[deft sail]

Are these identities right. I got them from sinx^2+cosx^2. Is it possible I get more?

[hoary totem]

line 5 should be sec(x) = √(tan²(x) + 1)

other than this it seems to be correct

[deft sail]

Thx

[grave pond]

Several of them have possible sign errors unless you restrict the range of x.

[hoary totem]

well yes u should add ± in front of all the square roots

[deft sail]

Is it necessary though? because people’ll automatically know that it’s ± anyway.

[hoary totem]

always good to make it explicit ¯_(ツ)_/¯

[grave pond]

If they already know what the correct thing is, why are they even reading your list?

[deft sail]

Idk

It’s just a scenario

[worthy acorn]

what identity would 2cos^2x = sinx +1 be?

[rustic kestrel]

the only thing that matters is

sin²x+cos²x = 1

and

sec²x = 1+tan²x

nothing more

just know these

and you will be better exactly

@deft sail

[deft sail]

[noble brook]

you can derive all of them from the Pythagorean theorem
you will get them all from dividing x² + y² =r² by x² y² and r²
for example
(x²/r²) + (y²/r²) = (r²/r²) so
cos²x+sin²y =1

[lime dune]

this is not an identity

looks like you might have been trying to use one of the double angle identities $2\cos^2 x=\cos 2x+1?$

[somber coyote]

elrichardo1337

[lime dune]

because it does not hold true for all x for which both sides are defined

[grave pond]

How do you get 486?

[vocal bison]

Equilateral triangle formula

[grave pond]

Hmm, you may have forgotten the other end of the prism.

[vocal bison]

Omg

Wait u right

Oop

[amber hollow]

what have i done wrong here

[dark sparrow]

your formula appears correct -- can you click on "help (entering your answer)"?

[amber hollow]

this just tells me to do it in the form of an equation

wait

it wanted f(x) not y, my bad

[dark sparrow]

yeah, was about to say

[steady sail]

@grave pond what is the lore behind your name because troposphere is a sphere of earth

[empty yew]

Is $\mathbb{R}-{n\pi+(-1)^{n}\frac{\pi}{6}} = \mathbb{R}-{(4n-1)\frac{\pi}{6}}$ ?

[somber coyote]

KingDanger

[empty yew]

Anyone clarify my doubt! Please!

[empty yew]

<@&286206848099549185> anyone help

[upper karma]

uh

[empty yew]

Is both the domains equal?

[upper karma]

sinx = 1/2

solve this for x

[empty yew]

Yes

[upper karma]

plot the graph

[empty yew]

While I am solving this (sinx=1/2) i got the second equation but my book say it's first so I am asking. is both equal?

[upper karma]

how did you get the second equation

[empty yew]

Just predicted by using unit circle i checked for two integers and it worked 😁

[uncut grove]

hi

can someone help me please

[empty yew]

!da2a

[lime crown]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[upper karma]

not same

[empty yew]

Mm thank you

[upper karma]

also first one is correct

[empty yew]

But how

[upper karma]

give it more deeper thought

sinx = 1/2

ok

means

[empty yew]

Ok

[upper karma]

sinx = sin(pi/6)

right

[empty yew]

Yes

[upper karma]

sinx - sin(pi/6) = 0

2sin((x-pi/6)/2)cos((x+pi/6)/2) = 0

did you get this

we used sum to product formula