geometry-and-trigonometry

[buoyant hinge]

no one around to help out a confused dad?

[dark sparrow]

yeah (1) gives you 25-odd million in^3

and you should only divide by 2150.42 once

does your textbook show the volume of the four cylinders in cubic inches being divided by a bushel thrice?

[upper karma]

@dark sparrow do you remember all these identities btw or do you look them up

[dark sparrow]

i happen to know them off the top of my head bc i've used them a lot

[upper karma]

i mean apart from cos(a+-b), sin(a+-b), cos(2a), sin(2b)

so you know for example like

sin x - sin y?

[faint cove]

My notes

[dark sparrow]

do you mean sin(x)-sin(y) = 2sin((x-y)/2)cos((x+y)/2)

[buoyant hinge]

@dark sparrow yes it does

[dark sparrow]

that's weird.

[faint cove]

However, I think you should see the derivations to understand them better

[dark sparrow]

uh

can you take a picture of what you're looking at @buoyant hinge

i'm just curious

[upper karma]

@dark sparrow damn you are a nerd

i can't remember that stuff at all

even tho i've only been learning for a week

trig

[dark sparrow]

i mean

no shit

[faint cove]

if u know the derivation u can logically know why it's like that

[dark sparrow]

a week ain't enough

[upper karma]

why not

[dark sparrow]

i've been doing shit with trig in one form or another for years

nothing wrong with not remembering stuff perfectly if you've only been at it for so little time

[upper karma]

i mean we've been doing them a lot tho over the past week

so idk

[dark sparrow]

seriously don't worry about it

[dark sparrow]

uh.

wow what

this is fucked up lmao

taken at face value, a bushel according to them is a unit of LENGTH, not volume!

[faint cove]

Lmao

[buoyant hinge]

I'm good with math.. no wiz or anything. I took calculus in high school but promptly forgot all of that. But pretty much anything under I'm pretty good with.. and I tried to reconcile what they had and couldn't figure out what they were doing to get there

Because if you calculate what they have written.... it doesnt even equal what they show

So I didnt know if I'd fallen further than I thought and was missing something vital

[dark sparrow]

yeah as i said

this is fucked up lmao

[faint cove]

If you’re worried, you can always check the dimensions/write them

Like this

Vtotal = 4πr²h
Vtotal = 4π(6 ft)²(32 ft)
Vtotal = 4π(36 ft²)(32 ft)
Vtotal = 14469.12 ft³
1 ft = 12 in
Vtotal = 14469.12(12 in)³
Vtotal = 14469.12(1728 in³)
Vtotal = 25002639.36 in³

Vtotal/bushel
= 25002639.36in³/2150.42in³
= 11626.86

The final dimension should be as what you expect

which here is no unit, because you’re just counting how many bushels fit in 4 cylinders

[buoyant hinge]

That's what he had as his answer. When I checked it and saw how far it was off, I looked at the teachers key and that's when my world started not making sense

Because to get their answer you have to divide 11626.86 by 3. And i have no clue why they did that... and not even show that's what they did

Thank you all for confirming for me that i didnt miss anything and their answer key is just wrong. Makes me highly suspect of the rest of it

[faint cove]

Just believe in yourself, books can be unreliable sometimes

[dark sparrow]

their answer is majorly screwed and your answer of 11626.86 is correct

[buoyant hinge]

Thanks. I've been wrong before, atleast according to my wife.

[upper karma]

can i get some help w/ this

idk this one at all lol

[faint cove]

Do you know what cos(α-β) equates to

[upper karma]

yes

[faint cove]

use it then

[upper karma]

ok

yeah ok i got nvm

[languid ingot]

There is question like: find sin (x/2), cos(x/2), and tan(x/2) for each set of conditions:
sin x = -3/5 and pi < x < 3pi/2

Ik how to plug in to the half angle formula thing. but how would i would like know if sin (x/2), cos(x/2), and tan(x/2) should have negative signs?

[silent plank]

use that they tell you about x to determine which quadrant x/2 is in

[languid ingot]

oh wait x/2 will always be in II quadrant?

[silent plank]

yes

[languid ingot]

okay is it same to assume:
if x is in first then x/2 is always in first
if x is in second then x/2 is always in first
if x is in third then x/2 is always in second
if x is in fourth then x/2 is always in second?

[dark sparrow]

why do you even need to assume anything

take pi < x < 3pi/2 and divide through by 2

or yknow any other quadrant info you may be given

why not do that instead of these weird heuristics

[languid ingot]

okay

[spiral niche]

think about it this way:

think of moving x around the circle and x/2 changing as x changes

when x gets to pi/2, x/2 is still trailing behind in the first quadrant

when x gets to pi, x/2 finally made it to pi/2, so any point less than pi results in x/2 in the first quadrant

as x continues to go around the circle, x/2 still remains in the second quadrant. when x gets to 2pi, x/2 finally made it to pi

[languid ingot]

okay

[dark sparrow]

espo that is honestly overcomplicated

like seriously

pi/2 < x/2 < 3pi/4

so x/2 is in the second quadrant

i don't understand why that's insufficient as far as clarity goes

[spiral niche]

some people work better with numbers

others work better with a geometrical understanding

telling someone "look, the numbers work out this way" doesn't always help

sometimes it helps to get an intuitive understanding of what's happening

[upper karma]

if i’m solving for cosine theta

and it gives me 2nd quadrant

is the answer going to be negative

cosine is (1,4) positive (2,3) negative

so cosine is forced to be negative

did i just answer my own question

can someone make sure im doing this right

[dire rampart]

didnt check the arithmetic but looks good

[upper karma]

bet

how do i find angle theta from the given cosine value?

that’s question 2

cosine is = .1736

do i do inverse?

[thorn talon]

Yes

[upper karma]

do i use sinh or cosh

[thorn talon]

Neither

Arccos or cos^-1

[upper karma]

oh

so 2nd function then cos?

WOAH 2nd function just opened up a whole world

[median crown]

it opens up the dark side of math

inverse trig

Eeeek

[upper karma]

in order to find csc theta

from cos

i have find sin right

like dat right

[limpid tide]

wouldn’t sin(theta) be -0.5?

[upper karma]

yeah u right

i forgot about the -

[limpid tide]

other than that looks good to me

[upper karma]

how do i calculate $\sin 6^\circ \sin 42^\circ \sin 66^\circ \sin 78^\circ.$

[somber coyote]

polynomial:

[limpid tide]

i’d just chuck em in a calculator

[upper karma]

@limpid tide yeah thats not the point tho....

i need to use some identities.

[limpid tide]

oh

i’d start with the sum and distance formulas, do you know those?

not distance, difference

sorry i’m very sleep deprived

[upper karma]

is it ok just to write this as .5

[limpid tide]

i mean probably unless your teacher’s a prick

[upper karma]

nah she’s cool

@limpid tide what do you mean sum and distance

[limpid tide]

sorry i meant sum and difference

[upper karma]

she does this stuff with margin of error

[limpid tide]

ok so

[upper karma]

sum and difference, you mean sin(a+b)?

if so yes

[limpid tide]

yes

okay

so first we have 6 degrees

can you think of standard angles that sum or subtract to 6?

[upper karma]

no?

@limpid tide what are they

?

probably a dumb question but to find tangent from a reference angle

i divide sine/cosine

with keep change flip right

because they’re both fractions

@limpid tide ??

dude

calm

he’s probably not on right now

pinging someone won’t make people respond faster

just probably piss them off

people have lives my dude

lol easy for you to say asking easy questions that anyone can answer in 5 sec

yeah that’s probably why people answer them

yeah so go away asking your easy questions when anyone can answer them and telling others as if their situation is the same lol

🤔

hmm

how would i find sine, cosine, and tan of -5pi/6

when that’s not an actual radical

idk how to make it one

can u not

im gonna assume i have to convert that radical to a negative degree

then switch that negative degree to a positive one

actually i think im stupid

i don’t know how to convert radicals to degrees

[upper karma]

<@&286206848099549185>

can anyone help me with my question above or

[marble topaz]

@upper karma back to what Sam said, think of angles that can get you 6
You already know quite a few special angles already, think about how you can relate them

@upper karma are you meaning to say radians? Just remember that pi radians = 180 degrees

And you can convert with that

[upper karma]

@marble topaz i mean, i know how to get 60, just not a "good" angle for both of the values

one of the values will be "bad"

[upper karma]

@a_nx^n + a_{n-1}x^{n-1} + ... + a_0

Why didn’t this tag you @upper karma ?)?

[glad falcon]

need help in voice chat.

[fleet wolf]

@upper karma i think you wrote the question wrong

[upper karma]

Yes

Ive been doing it

Tedious as fuck

There’s no way

This is correct

[fleet wolf]

the standard question has sums and differences not multiply

[upper karma]

question

@fleet wolf no... i didn't...

It’s actually fucked

to calculate sin(6)

@upper karma then you're doing something wrong

well i am too so idk lol

https://brainly.in/question/99473

@upper karma

This guy did it

Tedious as balls

the response below is like 4 lines

[fleet wolf]

hmm it seems like it is just multiple applications of sun to product

[upper karma]

how's that tedious lol

[fleet wolf]

yoo dont need to calc sin6 rudy

theres probs some shortcut

[upper karma]

Because that wasn’t the way I thought about it @upper karma ???

@upper karma

[upper karma]

is there a way to split any triangle into two right trinagles computationally

i know all of the sides (a, b and c)

[umbral snow]

@upper karma
I would suggest cos law to find an angle, then sohcahtoa once you're dealing with right triangles

[languid ingot]

@upper karma search up how to find altitudes of triangles

[wind heart]

Hey

I’m pretty sure I already asked this question and it was answered but honestly I forgot how to do it either way so here ;

How would I do #5?

[spiral niche]

What does it mean for two shapes to be similar?

[wind heart]

If they’re similar they have similar sides but not exact

I think?

[verbal summit]

i've got questions on how to do certain geoemtry problems wiith similar figures and dialations and i can send pics if i can be guided in the right direction on how to get the answer

@here

[deft ingot]

@verbal summit still need help?

[languid ingot]

@wind heart

to find the ratio, get the side of the first polygon, and then divide it by the second one with its corresponding side

so for your problem:

we know |AB| = 20. and |PQ| = 25 because |SR| and |PQ| are congruent

thus we need to just do: 20/25 or 20:25, which would simplify to 4:5

so now we have the ratio we can just multiply it by the original one to get the second one. for e.g.,
|AD| = 14, so |PS| = 14*(4/5) = 11.2

[wind heart]

Hello

Thanks

[languid ingot]

np

[clear falcon]

where did they get angle ABC and ABD is a right angle?

[jade solar]

If they are right angles then B will lie on CD right?

[clear falcon]

nvm i got it

[blazing panther]

How to find tan and arctan using unit circle

[dark sparrow]

draw the tangent line to the circle at the point (1,0), a.k.a. the line x=1. call it "the tangent axis"

for all θ that aren't π/2 or 3π/2, the line passing through θ's point on the unit circle (i.e. (cos(θ), sin(θ))) and the origin will intersect the tangent axis at one and only one point

the y coordinate of this point is tan(θ)

does that answer your question or would you like an illustration

@blazing panther

[dark sparrow]

👻

[dire rampart]

👻

[upper karma]

how do i calculate radius from degrees in my calculator

like

451°10'

Texas TI 84 plus ce-t

[marble topaz]

@upper karma recall that 180 degrees is equal to pi radians

That should enable you to convert pretty easily

[upper karma]

in calculator?

[dark sparrow]

"radius" did you mean radians

are you trying to convert 451°10' to radians

bc that'll be (451 + 10/60) * pi/180

[upper karma]

oh yeah I got that

i see what I was doing wrong

I got 7.87434 rad now

🙂

ty for help

This can only be done through calculator right?

[dark sparrow]

wdym

[upper karma]

Formula can be written, but the calculating, through calculator right?

[dark sparrow]

unless you're allergic to calculations with four-digit numbers

[marble topaz]

You could absolutely do it w/pencil and paper

[dark sparrow]

you can do the calculation by hand just fine

it's gonna be a bit painful but it's absolutely doable

[upper karma]

let me try

okay i might not do it if it's painful

xd

I can use calculator on tests, so I guess i'll just stick with that

[hot pumice]

How do I deal with a question like this when there are no solutions?

Hope this is the right channel

[dire rampart]

why do you say there are no solutions

[hot pumice]

Sorry, meant infinitely many solutions

[spiral niche]

@hot pumice say what y has to be in terms of x

so in this case, y = x

but sometimes y might have to be 4x

or nx

so y=nx, where in this case n = 1

[hot pumice]

Ahh right I get it, ty

[upbeat trail]

In sin(x), sinh(x), arcsin(x) and arcsinh(x).. Is the x in rad or in degree?

Mention me if someone answer

[weary drift]

@upbeat trail it doesn't make sense to plug in angle measurements into the arc trig functions... as for the non arc functions, either are fine

[upbeat trail]

Alright thanks

[dense sky]

Can I math god help me complete the squares with circles

[silent plank]

what issue are you having with completing the square?

[verbal summit]

if there is 5 green and 7 yellow pencils the chance of getting 2 yellow pencils is 16%?

[umbral snow]

Pulling them from a bag without replacement?

,calc (7/12)(6/11)

[somber coyote]

Result:

0.31818181818182

[flat spruce]

#probability-statistics

[verbal summit]

anyone good with probability

[spiral niche]

Ish

I can probably help

and if I relearn something, cool

[clever heron]

hey so i have an easy question about circles and arcs but i forgot all the properties of arcs would this be the place to ask

[limpid tide]

presumably

[clever heron]

cool

how would i find the measure of angle D and angle A

my old math binder fell apart so i lost all my notes on arcs, no other info given in the problem

[glad falcon]

what is

70deg and what is 80deg

i am having trouoble figuring out the diagram

[lyric summit]

i am having trouble figuring out this problem

sorry its blurry

[fringe crater]

Hey @lyric summit, so if you want to find the distance between M and N, you can try to visualize some squares in the diagram, like this:

[dusky cobalt]

Yea

[lyric summit]

oh

[dusky cobalt]

Jessi make

Squares

[lyric summit]

why r heRe

[dusky cobalt]

Then you can make the hypotenuse

Root 2

[lyric summit]

ok

[dusky cobalt]

Welll

Multiply by root 2

Do that for both

Then add

And

Booom

Big brain

Right there

[lyric summit]

and is it 12

[dusky cobalt]

Wait

Uhm

[lyric summit]

its root 320

ok

[dusky cobalt]

Wait

Jessi

[fringe crater]

I got 24*sqrt(2)

[dusky cobalt]

Yea

Wait

Leemee

Yea

16 plus 8

Is 24

[lyric summit]

oh

[dusky cobalt]

But theres also a root 2

Yea

So 24 root 2

[lyric summit]

thx both of yall

[dusky cobalt]

:)))))

[fringe crater]

yw 🙂

[lyric summit]

:)

[twin prawn]

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

[wind heart]

Hi

How do I complete 6 7 and 8?

Let’s see

Does is 6. 15, is 7. 60, and is 8. 8?

[spiral niche]

7 isn't 60

[wind heart]

Oh

How so

Oh wait

Is it 18?

[spiral niche]

Yes!

[wind heart]

Oh perfect

So is everything else right

(6,7,8)

Not the others

[spiral niche]

yes, 6 and 8 were correct

[onyx basin]

quick question

for arcsin x = theta, why is it restricted to the first and fourth quadrants of the unit circle

[weary drift]

arcsin is defined as the inverse of sin where sin has been restricted to the interval [-pi/2,pi/2]

[spiral niche]

think about it this way:

[noble coral]

URGENT

[spiral niche]

do you remember the definition of a function?

[onyx basin]

my brain is like failing rn

yea

[spiral niche]

for every one input, there one output

never more than one

[onyx basin]

mhm

[noble coral]

HOW WOULD I FIND THE RAIDUS OF THIS CIRCLE please

[spiral niche]

sin takes in any angle

[onyx basin]

mhm

[spiral niche]

do you know what the range of sin is?

like the function?

how do I graph

,graph sin(x)

[onyx basin]

-1 to 1 right

[spiral niche]

yeah

[onyx basin]

$,graph sin(x)$

[somber coyote]

analyst:

[spiral niche]

lol

[onyx basin]

yes thank you texit

[spiral niche]

it's always -1 to 1

[onyx basin]

mhm

[spiral niche]

however, if arcsin(x) is going to be a function, it can only give one output for every input

so if you want to know where sin(x) = 1

you do arcsin(1)

but it can only give one output

[onyx basin]

mhm

[spiral niche]

even though sin(x) = 1 at pi/2, 5pi/2, 9pi/2, etc.

so it only gives the answer that's in quadrants one and four

[onyx basin]

ohhh

yeah okay

lmao

ty

[spiral niche]

does that make sense?

[onyx basin]

mhm

[spiral niche]

@noble coral

I have an answer for you, but it's not rigorous

like it isn't a proof, but it gives you the answer

since the large box is 6x6, you can put 9 2x2 boxes in it

the middle box is going to have one corner touch the bottom left box and one corner touch the center of the circle

and the radius of that box is going to be

[noble coral]

yes

[spiral niche]

which is the radius of the circle

wait that might be wrong

[noble coral]

Uhm

Can u draw it out please

[spiral niche]

ah wait wtf

it is 2 or 2root(2)

[noble coral]

Can u draw out the solving please

Cuz I cant understand

[spiral niche]

wait my answer is wrong

[deft ingot]

Use both diagonals

The little square and the big square

After, find the diameter

[noble coral]

ok

I did this

I’m not sure if it’s right tho

[deft ingot]

Wait..

Thinking better

[noble coral]

but we aren’t given if the TOP square box is a square

[deft ingot]

The problem is the little segment

[noble coral]

yea

[deft ingot]

But, maybe you can use pythagoras

[noble coral]

ya how

Can u explain

Or like solve

[noble coral]

Uhm I don’t get it

[deft ingot]

sqrt(2) × (4 - r) = r

The middle triangle is a 45 45 90 with hypothenuse R and sides 4 - R

[noble coral]

Yes

The sides are 6

And hypotenuse is 6root2

[deft ingot]

I drawed another triangle, can hou see it?

[noble coral]

So uh what’s the answer?

[deft ingot]

r = 4× sqrt2 / sqrt2 + 1

[noble coral]

Uh

So

Uhm

Ok

LOL I DONT GET IT

so hard!

[noble coral]

@deft ingot

ok

im really sorry

but can u explain it to me step by step

I beg you

Im soooo so sorry

[deft ingot]

hmm

[noble coral]

like starting from the first picture

[deft ingot]

see that middle triangle i made?

[noble coral]

yes

wait

also we aren't given that the top box is a square

[deft ingot]

Which box?

[noble coral]

but I asked some guy and he said that it was a square cuz of the point at the raidus

look

[deft ingot]

Yeah it is a box

[noble coral]

https://cdn.discordapp.com/attachments/326138757474680852/682066060836732961/image0.jpg

yea

so

[deft ingot]

Middle triangle i made there

Hypothenuse is R

their sides is 6 - 2 - R

Do pythagoras

[noble coral]

what do u mean

how is it 6-2 - r

[deft ingot]

hmm

let me draw

[noble coral]

ok

[deft ingot]

See it now?

[noble coral]

yea what about it

no so what did u get

for the radius

whats the answer

[deft ingot]

r = 4× sqrt2 / sqrt2 + 1
@deft ingot

[noble coral]

where does the one come from

[deft ingot]

R + Rsqrt2 = 4sqrt2

[noble coral]

ok

i got it

thank u sm

[deft ingot]

[lofty scaffold]

How do we pronounce\
$\arcsin 0.5$

[somber coyote]

PristineWolf:

[twin prawn]

How would you pronounce it

[umbral snow]

arc sine zero point five

Or pi over 6

[lofty scaffold]

π/6

How

[umbral snow]

Jk about that part

[lofty scaffold]

Lmao don't joke in trig pls

[weary drift]

except kaynex isn't really jk'ing

[lofty scaffold]

You'll mess with the 9th grader's brain

:(

[umbral snow]

I am in the sense that you wouldn't pronounce that like that

[lofty scaffold]

Rokabe I wanna ask you some stuff but awk

Imma finish reviewing for tomorrow's French test and I'll come back

[silent plank]

'bad' questions get 'bad' answers

[lofty scaffold]

Me?

[silent plank]

what else were you expecting other than

arc sine zero point five

[lofty scaffold]

I just wanted to know if the part "arc" in arcsine was pronounced the same or smth diff

[silent plank]

just read it normally

[lofty scaffold]

Well you don't read "cos"

Lmao if you say cos in my country it is REALLY close to a swear word here

😂

[twin prawn]

cosine

[umbral snow]

I only ever read cos

[weary drift]

when speaking fast i pronounce cos as cuss

[umbral snow]

But I also read sine

[twin prawn]

saying sin is a sin

[lofty scaffold]

Imma gtg n come back

[silent plank]

shine for sinh is quite fun

[weary drift]

you say shine instead of sinch?

[silent plank]

yeh

[weary drift]

what about cosh

[twin prawn]

cosh

[silent plank]

just cosh for that

[weary drift]

tanh?

[silent plank]

(th)an or fan?
been a while

[twin prawn]

"tan AITCH"

[silent plank]

don't think i've ever had to pronounce it

[weary drift]

never heard of than or fan, interesting

[twin prawn]

"hyperbolic tangent"

[weary drift]

i pretty much go with how khan would say it

[silent plank]

thfan nfi, how to transcribe that fkn sound

i'll look up some vids

[weary drift]

thfan sounds like so much effort

[silent plank]

geez that first vid when i searched it was horrid

[keen rose]

guys this last question is one of those (whats 2+2 hense solve the surface area of the moon) type questions

[silent plank]

um what?

[weary drift]

expanding & using trig identities may get you somewhere

[keen rose]

i know like 2 trig identities

and i dont know where to begin

[weary drift]

expanding

[keen rose]

but how do i get a vlue

because theres no value of theta

[silent plank]

which trig identit(ies) do you know?

[keen rose]

thats what confuses me

as in like the rules

sin^2x + cos^2x = 1

[silent plank]

not tan(x)

[keen rose]

1

oops

i merged them

is it cos/sin = tan?

[silent plank]

no

sin(x)/cos(x) = tan(x)

[keen rose]

ye that

[silent plank]

sin^2x + cos^2x = 1
in addition to basic exponent/distribution laws
should be all that you need

[keen rose]

ohhh

shoot ye

ok ill give it a go and come back

if i fail

[upper karma]

is this right

or am i just dumb

[quiet mason]

no you confused D with sine(D)

[silent plank]

(and d with D)

[upper karma]

uh

so what i am supposee to do

to find the d value

[quiet mason]

use a calculator

or write arcsin(that fraction)

,w arcsin(68/85)

[somber coyote]

Display results online and refine query

Requested by NoaH#5497

[upper karma]

uh

im leaerning special angle

i dont think my teacher was asking for that

oh

thats radian

thats why

@upper karma special angle ez

yeah but then

[silent plank]

this isn't a special angle

[upper karma]

WHY WOULD MY TEACHER

put this in

a google docs

if it wasnt special angle

Can’t you find it with Inverse sine

**Special Angles and Unknown Angles **

Yea

the thing is we haven't learned how to use einverse sinee

Fr?

yep

Just use calculator it u can

[quiet mason]

then just write arcsin(that frac)

[upper karma]

i have my casio in

[quiet mason]

then, i guess

[upper karma]

i mean out

hm

aren't we suppose to use

trig ratio

to solve this problem

[silent plank]

you apply the trig ratio to set up your initial equation

sin(d) = opp/hyp = 68/85

[upper karma]

hold on

so

what if we dont know the trig ratio

how do we solve

[silent plank]

wdym if you didn't know the ratio?

[upper karma]

so are we suppose to find the trig ratio

using all of the length of the sides?

[silent plank]

since you're given all 3 sides you can use whichever ratio you want

the ratio would only involve 2 sides

[somber coyote]

PristineWolf:

Can we call this $\arcsin$ sin inverse

[lofty scaffold]

Or is it just for sin^-1

[upper karma]

i got it

thanks

[weary drift]

arcsin & sin^-1 refer to the same function. Referring to either as inverse sin is misleading. Remember that talk I gave about making a certain restriction on the domain of sin in order for it to be invertible

[lofty scaffold]

rokabe..

Pls

Give me a moment then

Lemme finish math hw n come

Guess we're not ending

[weary drift]

I won’t relent til you stop asking trig qs

[lofty scaffold]

So you mean you're not leaving me confused?

[dark sparrow]

[lofty scaffold]

@weary drift

[weary drift]

你要什么？

[lofty scaffold]

Can you explain them again

Pls

[weary drift]

[rain oracle]

Hello. I have 2 questions. I want to ask my first question;

The number of pi can be 3.14 or 180. Is pi's 3.14 value in radians or degrees?

I have researched in many sources, many say different things

[weary drift]

You can never truncate digits of pi and still have its exact value. Almost never do it. pi is approx 3.14 but not 3.14

pi is the ratio of a circle’s circumference to its diameter. And pi radians = 180 degrees

[dark sparrow]

The number of pi can be 3.14 or 180.
no

any resource that says "pi = 180" outright is not a resource ever worth reading

[rain oracle]

pi radians = 180 degrees. I don't understand this sentence. pi radian must be equal to a radian value, right?

[weary drift]

rad & deg are units describing angle measurements. The above relation gives how to convert between the two units

[dark sparrow]

^

in that sense, it's no different than saying "1 foot = 12 inches"

[rain oracle]

In other words, does pi number have 2 values ​​as degrees and radians?

Can we use the number pi in radians or degrees

I'm so confused 😄

[dark sparrow]

no, you're overthinking it

pi is pi. it's a number. it's equal to the circumference of a circle whose diameter is 1.

it's approximately equal to 3.14159. and that doesn't depend on what units are attached to it.

radians and degrees are units of angle

it's not like "pi degrees" is not a valid angle for whatever reason

you can have a length of π meters, a timespan of π hours, a volume of π liters, whatever

[rain oracle]

sometimes we could write 180 instead of pi. I am trying to understand the logic of this

[dark sparrow]

if you see it as "writing 180 instead of pi" then there is no logic to it

because pi and 180 are two very different numbers. they differ by about 176.86

[rain oracle]

I've never seen trigonometry before. I'm trying to understand some things myself😄

because i need this informations about trigonometry

can i post a photo here?

@dark sparrow

[dark sparrow]

sure

[rain oracle]

I think I need to know what this is first

[idle bloom]

Ok so

ignore the stuff in the middle

do you understand what's going on on the circumference of the circle?

[rain oracle]

No 😄

[idle bloom]

ok

So it's a new way of defining angles

we're used to degrees

360 degrees in a circle correct?

[rain oracle]

Yes

[idle bloom]

but it's kind of arbitary, 360 just happens to divide into alot of nice factors so it's useful in that way

but it's still arbitrary

this other system uses a unit called a radien

which you'll notice is really really close to the word radius

the definition of a radien is that if you take the radius of a circle and lay it out on the circumference of the circle

it'll sweep out some angle

and that angle is 1 radien

there are 2pi radiens in a circle

so if I take the length of a radius

r

and multiply that by 2 pi

i'll have swept out a full circle

which makes sense, because the circumference of a circle is 2pi*r

take some time to read out what I wrote and if you're still confused lemme know

[rain oracle]

Can we say 1 radian = radius?

Okay okay im understand 😄

[idle bloom]

well more exactly

the angle swept out by laying 1 radius on the circumference is 1 radien

[dark sparrow]

there's a gif for this, hold on

https://upload.wikimedia.org/wikipedia/commons/4/4e/Circle_radians.gif

[rain oracle]

Oooohhhhh

İts superrr

Thank you

So π is the half part of the a circle

[idle bloom]

pi radiens is half a circle yes

[rain oracle]

Pi radiens

[idle bloom]

just like how 180 degrees is half a circle

360 degrees = 2pi radiens

[rain oracle]

Okaaay so a pi radien=180 degree

Right?

[idle bloom]

yes

that's how you convert between the two

[rain oracle]

man thank you very much

[idle bloom]

both of them are angle measurements

[rain oracle]

And you too @dark sparrow

[dark sparrow]

yw

i've had the most success with this one gif compared to all other materials

[verbal summit]

Can someone help on how’d I go about doing this

I want to say so far this is right

[silent plank]

b,c are wrong

[verbal summit]

Is b 35 and c 145

[silent plank]

yes

btw make sure to include °

[verbal summit]

K

How would I get l and o

[silent plank]

same methods as what you were doing before
the horizontal bars are extra thick but just treat like every other line

[verbal summit]

So it’s just 110

For l

[silent plank]

° yes

[verbal summit]

And than 70 for o

[silent plank]

yeh

[verbal summit]

K

Is k and n 65

[drowsy walrus]

n is not 65

neither is k

[verbal summit]

Is it n 60 k 70

[drowsy walrus]

yeah

[verbal summit]

Can u check the bottom for me

[drowsy walrus]

B and C are incorrect

[verbal summit]

Than how would I get it if I don’t do 180-39

[silent plank]

B + 39° + 47° = 180°

B and 39° aren't the only angles on that line

[verbal summit]

So 94

[silent plank]

yeh

[verbal summit]

Where would I start on this side

[drowsy walrus]

Vertical angles

[silent plank]

why did you erase those 48°s

[drowsy walrus]

actually y is supp to 132

[silent plank]

same idea as the other parts you've just completed

[verbal summit]

48 didn’t seem right

[drowsy walrus]

why not?

[silent plank]

^

[verbal summit]

Just didn’t

But why is y 132

[silent plank]

Y isn't 132

[drowsy walrus]

It’s not

It’s supplementary to 132

[verbal summit]

Oh lmao

So 48?

[drowsy walrus]

Yes

[verbal summit]

And 180-85=a?

[drowsy walrus]

where did you get 85

[verbal summit]

180-47-48

[drowsy walrus]

also, if you know that alternate interior angles are congruent and corresponding angles are congruent, you’re pretty much done

[verbal summit]

Is it 132?

[silent plank]

is 'what' 132?

[verbal summit]

z

And a is 48

[drowsy walrus]

yep

[verbal summit]

Well there’s a d and it’s out of place I think it’s 21

[silent plank]

where?

[silent plank]

c is still wrong

[verbal summit]

How

[drowsy walrus]

b and d are wrong as well

[silent plank]

b and d are right

[drowsy walrus]

oh

my bad

[verbal summit]

Is it 86

[drowsy walrus]

yea

[silent plank]

be careful with which lines are actually parallel when applying the alt angles theorem

[verbal summit]

So what about d

[silent plank]

D = 94° is fine

[verbal summit]

D not b

[silent plank]

B = 94° is also fine

[verbal summit]

So is d 94

[silent plank]

capital D

yes

[verbal summit]

How’s it 94

[drowsy walrus]

all angles in a triangle add to 180

[silent plank]

alternate angles on parallel lines.
also ^

if you calculated E first

and all those should be consistent

[verbal summit]

Oh I ment the other d mb

Or is it p

Ugh

By q and o

[silent plank]

the ones in the centre area?

[verbal summit]

Ya

[silent plank]

well firstly r is wrong

be careful with which lines are actually parallel when applying the alt angles theorem

[verbal summit]

68 r

[silent plank]

yes

[verbal summit]

So what about p it’s on a line with 5 which don’t make sense

[silent plank]

and also the number of angles that are on the line

wdym on a line with 5?

[verbal summit]

The p is on a line with 5

[drowsy walrus]

5 other angles?

[silent plank]

thats an s

[verbal summit]

O...

[silent plank]

you need to find that angle too

[verbal summit]

So it’s 157 s and 23 p

Okie dokie

[silent plank]

yeh

[deep pewter]

$sphere: (x-1)^2+(y-2)^2+(z+1)^2=9 \ curve: l(t)=(1+t,2+t^2,3+3t^2), \quad t\inℝ$

how do I find the shortest distance from the sphere surface to the curve?

[somber coyote]

Squik:

[high phoenix]

Does anyone know shortcuts for the problem
Cos(x+pi/4)-Cos(x-pi/4)

I’m looking for things that I can cancel instead of having to do two product to sum formulas

[silent plank]

did you mean sum to product?

you should only need to do it once

(also quite simple to apply angle sum identities, which is where those formulae are derived from)

[high phoenix]

What are angle sum identities? Like double angle and half angle identities?

[silent plank]

sin(a+b) =

etc

[high phoenix]

Isn’t that Sin(a+b) = Sin(a)Cos(b)+Cos(a)Sin(b)?

[silent plank]

lower case, but yes

that is an angle sum identity, or similar name (compound angles)

[high phoenix]

Yea, are there any shortcuts for those, so I don’t have to do the whole formula?

I would imagine that there is a shortened version of those

[silent plank]

the 'shortcut' for that specific question would be applying the
sum to product identity directly

[high phoenix]

How exactly is that done?

[high phoenix]

Whoah, that’s wack

[silent plank]

and this is also a special case

$\cos(x + y) - \cos(x-y) = -2\sin(x)\sin(y)$

[somber coyote]

ramonov:

[high phoenix]

Ah, I gotcha. I solved it but it took a lot of legwork

[tall flower]

guys can someone help me w/angular velocity

please

[drowsy walrus]

just send your problem

[upper karma]

@drowsy walrus ya able to help me out?

[wind heart]

How would I find 2-6, 10, and 12-14 ( I don’t understand the work)

Like, how am I supposed to know which side to set the side equal to?

(For some of them)

[upper karma]

Can any of ya'll help me on how to do this?

[drowsy walrus]

if another question has been posted, please use one of the channels under math help

@wind heart just across the two transversals. the other lines are parallel, so use the line-splitter theorem

[wind heart]

Like

For 10

I’m kinda confused why it’s not

5/6 = 9/7.5

Like why are the 5 and six flopped

It’s weird

[drowsy walrus]

Be careful

Keep in mind that if you set the proportion up from bottom line to top line, you set that other proportion the same way; bottom to top

[wind heart]

Do then 10 is incorrect?

It isn’t “Yes”?

[drowsy walrus]

10 on the screenshot is correct

[wind heart]

But they aren’t doing it bottom to top

Oh wait

How

Did I

[drowsy walrus]

the other doesn’t matter, just as long as the corresponding parts are the same

[wind heart]

Not

See that

[drowsy walrus]

order*

Yeah lol it’s pretty challenging

[wind heart]

So like

For 2-6

Each side is congruent right

Like

How does number 3 make any sense

[drowsy walrus]

2-6 is correct, yes

well, you can look at it from different ways by moving the proportion around

[wind heart]

Is CD like

Half of FB

or smth

[drowsy walrus]

$\frac{CD}{FB}=\frac{GD}{GB}$ can be rearranged to become $\frac{CD}{GD}=\frac{FB}{GB}$ or any way that helps you see it

[somber coyote]

xItzDia:

[wind heart]

That’s really weird

[drowsy walrus]

if you cross multiply, the products should all match the original

but look at it from across, not up and down

Notice that CD and GD line up and FB and GB line up

[wind heart]

Look at everything from across?

[drowsy walrus]

yes

[wind heart]

I kinda see it

Oh I’m seeing it now

Now let me see if I get 12-14 or not

[drowsy walrus]

Kk

[wind heart]

Yeah I don’t get it

oof

[drowsy walrus]

You set them up right

Just cross-multiply

and solve like you would for any other variable

[wind heart]

Hmmmm

[mossy shoal]

@wind heart

if u get confused about tf does parallel lines mean

Think back to slope

y = mx

[wind heart]

Oh I see

[mossy shoal]

If u have 2 slopes
m1
m2

Theyre parallel if theyre equal

[wind heart]

That’s a different way of putting it

[mossy shoal]

Jst make sure u consistent with how u comparing proportions

Or u gon goof and get wrong answer

[wind heart]

Thanks

[upper karma]

Question guys

This is a physics problem but uses trig

It’s a calculation for acceleration down a slope so a=(5/7)(g)(sin(theta))

So why the 5/7 part?

[mossy shoal]

F = ma

we cant say shit unless we see free body diagram

or know more about problem

Like forces in every dir

starting from rest or wat

[upper karma]

Ah. I guess that’s why we were spoon fed that equation lol

We were doing an experiment on acceleration of a marble down a slope. It’s just the 2nd lab so far

I’m guessing the 5/7 has to do with friction and mass maybe? Like a friction coefficient?

[languid ingot]

The park has the shape of a quadrilateral. Three sides measure 50, 60, and 70. The angle between two sides of 50 and 60 is 127 degrees. The angle between 60 and 70 is 132 degrees. How can I find the fourth side's side and the size of the quadrilateral?

I found it nvm

[lofty scaffold]

Hey

Can someone see if I'm right?

$\frac{1}{\cos\alpha}$ is reciprocal of the cosine\
$\cos^{-1}$ OR $\arccos$ is inverse of the cosine

[marble topaz]

arccos and 1/cos are not the same thing

[lofty scaffold]

arccos and cos^-1 are not the same?

How

[marble topaz]

No

[lofty scaffold]

WTF

[marble topaz]

Oh no I see

[lofty scaffold]

How

[marble topaz]

Mathematical inverse and notational here are two different things

Cos to the negative 1 (1/cos) is actually the function secant

arccos and secant are not the same thing

The normal notation of cos^-1 is just a conventional quirk

[lofty scaffold]

Rokabe told me when we say cos-1 we never mean secant

[weak shoal]

Yes he's not wrong

[marble topaz]

Yes exactly

But cos^-1 is NOT 1/cos

[weak shoal]

cos^(-1) and arccos are the same thing

1/cos is the reciprocal of cos

[lofty scaffold]

Yes that's what I wanted to make sure of

Vats better?

[weak shoal]

But if you have: $\cos^n(x)$, that's the same thing as $(\cos(x))^n$

[somber coyote]

Abhijeet Vats:

[grim halo]

no

wait yes

[weak shoal]

Inverse of the cosine

Yes, that's correct

[grim halo]

but the second one isn't the correct notation right?

[weak shoal]

And 'reciprocal of the cosine'

[marble topaz]

Second one is totally valid

[weak shoal]

Second one is correct.

[grim halo]

really, I got marked off for doing it

[weak shoal]

Anyways, people tend to use arccos

[grim halo]

guess its just a teacher quirk

[weak shoal]

Cos it's less confusing

[marble topaz]

Cos

[weak shoal]

Tell your teacher to suck a dick

[marble topaz]

Hehe

[somber coyote]

PristineWolf:

[weak shoal]

Yes that works

[lofty scaffold]

K so the first line is when

We STILL HAVE THE ANGLE

[weak shoal]

Keep in mind that restrictions need to be made such that the inverse actually exists

[marble topaz]

Yep, 1/cos spits out a ratio
cos^-1 spits out an angle

[lofty scaffold]

And the 2nd is when we will use inverse of cosine to get the angle

[marble topaz]

Exactly

[lofty scaffold]

I think I got it

[grim halo]

in precalc I had to graph arccos, sad times 😦

[weak shoal]

Keep in mind that the angle interpretation is limiting

[lofty scaffold]

Vats

Hold up for. Asecond

[weak shoal]

These are just functions with specific definitions

[marble topaz]

Maybe I should stop talking

[lofty scaffold]

For this year teacher said only actute angles no 0° no 90°

[weak shoal]

Nah bandana lol, i'll let you take this one

[lofty scaffold]

So don't sweat on me

[grim halo]

i think thats because you get to those in algebra 2

[marble topaz]

Ah, so you won't even be worrying about the domains of the inverse trig functions

[grim halo]

i still get confused on that

[lofty scaffold]

@weary drift why did you overcomplicate it to me 1st year trig and I still have no clue what domains / images are. Will probs study 'em later the summer

[marble topaz]

Thank their periodicity for that one

[lofty scaffold]

Thanks rokabe tho <3

[weak shoal]

Don't worry, perspiring on you is the last thing I'd want to do 😄

[marble topaz]

Pff

[grim halo]

domains are just x values that are allowed

basically

[lofty scaffold]

Like intervals?

[grim halo]

kinda

[lofty scaffold]

Nvm

[weak shoal]

He didn't overcomplicate anything. He just said the truth as it is.

[lofty scaffold]

But 9th grader brain

[marble topaz]

They're exactly like intervals

[lofty scaffold]

Too tiny

[grim halo]

I had to graph arccos and I got marked off for "wrong work"

[marble topaz]

A function is defined on the interval x=whatever

[weak shoal]

Forget it. Understanding domains and codomains requires a bit of work with sets.

[grim halo]

because arccos technically doesn't have a midline

i got so mad

[marble topaz]

Sorry, a midline?

Oh you're talking about the point where it's undefined

[grim halo]

she literally taught us to use a midline but we get marked off for it

[weak shoal]

So forget about it for now. Once you reach the topic of functions, then worry about it.

[marble topaz]

Oh wait vats is this pre-precalc stuff?

[grim halo]

?

[marble topaz]

Shoot sorry, okay I'll drop the functiony talk

[lofty scaffold]

I did not understand anything 😂

[grim halo]

oh, that's more algebra 2