Trig | Mathematics | Page 1

storm mantle Oct 28, 2022, 5:43 AM

#

Trig

#

@runic estuary

#

Sorry, I'm not quite comfortable with friending people I don't know in person

runic estuary Oct 28, 2022, 5:43 AM

#

its ok

#

so the thing im supposed to do now is find -3pi/4

#

and so that should be a 45 45 90 triangle when you draw the reference angle and connect it all and do make all the triangle math happen

storm mantle Oct 28, 2022, 5:45 AM

#

That'll be at 5pi/4

runic estuary Oct 28, 2022, 5:46 AM

#

yeh i know that but why do these all do different things

#

#

#

GRAH

#

IM SO CONFUSED

#

THE NUMBERS ARENT SUPPOSED TO LIE

storm mantle Oct 28, 2022, 5:47 AM

#

I couldn't find one for 45 degrees, but here it is for 30

#

storm mantle Oct 28, 2022, 5:48 AM

#

runic estuary

Here the hypotenuse is sqrt(2), not one like the radius of the circle

runic estuary Oct 28, 2022, 5:48 AM

#

oh 🤔

#

oh so i was looking at the wrong triangle

#

DAMMIT BROCCOLI

storm mantle Oct 28, 2022, 5:49 AM

#

It's fine, I thought the same thing at one point

runic estuary Oct 28, 2022, 5:49 AM

#

wait a minute

#

so

#

sqrt2/2 isnt the sin or cos its just the length of that side right?

storm mantle Oct 28, 2022, 5:51 AM

#

sin(45 degrees)=sqrt(2)/2, and cos(45 degrees)=sqrt(2)/2, which corresponds to the side lengths

#

Cos(x) will correlate with the horizontal line, while sin(x) will correlate with the vertical line

runic estuary Oct 28, 2022, 5:52 AM

#

so if sin is opposite over hypotenuse then why isn’t it sqrt(2)/1

#

idk if that makes sensr

#

sense

storm mantle Oct 28, 2022, 5:52 AM

#

I get it

#

It'd actually be $frac{frac{\sqrt(2)}{2}}{1}$

stone havenBOT Oct 28, 2022, 5:53 AM

#

Orthodox

storm mantle Oct 28, 2022, 5:53 AM

#

That didn't work

runic estuary Oct 28, 2022, 5:53 AM

#

oof

storm mantle Oct 28, 2022, 5:54 AM

#

$\frac{\frac{\sqrt(2)}{2}}{1}$

stone havenBOT Oct 28, 2022, 5:54 AM

#

Orthodox

storm mantle Oct 28, 2022, 5:54 AM

#

Which is still $\frac{\sqrt(2)}{2}$

runic estuary Oct 28, 2022, 5:54 AM

#

oh wait

stone havenBOT Oct 28, 2022, 5:54 AM

#

Orthodox

runic estuary Oct 28, 2022, 5:54 AM

#

yeah

#

Ok NOW im getting a tiny piece of the puzzle

#

dammit broccoli!!!

storm mantle Oct 28, 2022, 5:56 AM

#

I'll try and draw something out quickly

runic estuary Oct 28, 2022, 5:56 AM

#

so opposite is the Y line and adjacent is the X line?

storm mantle Oct 28, 2022, 5:57 AM

#

Yes

#

#

So here opp/hyp would be sqrt(2)/2, which makes sense with sin(45)

runic estuary Oct 28, 2022, 5:59 AM

#

yeee

#

wait so

#

nvm i thought out the question

storm mantle Oct 28, 2022, 6:00 AM

#

Nice, being able to figure something out on your own is always a nice feeling

runic estuary Oct 28, 2022, 6:00 AM

#

it is

storm mantle Oct 28, 2022, 6:00 AM

#

But of course never be afraid to ask questions

runic estuary Oct 28, 2022, 6:01 AM

#

i feel so bad when it comes to math cuz i went to tutoring for like 8 months last year snd and learned like nothing

#

2 times a week too

storm mantle Oct 28, 2022, 6:02 AM

#

Ah, tutoring sometimes isn't the best method for everyone

#

Probably wouldn't work well for me, personally speaking

runic estuary Oct 28, 2022, 6:02 AM

#

wait so

#

for cosecant i got 1/sqrt(2)/2 and the same for secant

#

is thst right in this problem?

storm mantle Oct 28, 2022, 6:03 AM

#

That should be, although it can be simplified

runic estuary Oct 28, 2022, 6:03 AM

#

how do i simplify it

storm mantle Oct 28, 2022, 6:04 AM

#

If you have $\frac{1}{\frac{\sqrt(2)}{2}}$

stone havenBOT Oct 28, 2022, 6:04 AM

#

Orthodox

storm mantle Oct 28, 2022, 6:05 AM

#

The very bottom number, the 2, can be taken up to the top

runic estuary Oct 28, 2022, 6:05 AM

#

ahhhh i was about to do that ong

#

oh but then what do i do with the exponent

#

does it cancel out the radical and make it 1/2

#

oh i should also say the radical is -2

storm mantle Oct 28, 2022, 6:06 AM

#

Here you'd have $\frac{2}{\sqrt(2)}$

stone havenBOT Oct 28, 2022, 6:06 AM

#

Orthodox

runic estuary Oct 28, 2022, 6:06 AM

#

ohhh

#

i thought u meant like an exponent

#

oof

storm mantle Oct 28, 2022, 6:06 AM

#

runic estuary oh i should also say the radical is -2

For sin(-3pi/4) yes

runic estuary Oct 28, 2022, 6:07 AM

#

so why do you get to do that

#

move the bottom to the top

storm mantle Oct 28, 2022, 6:08 AM

#

That's a good question, I'd never really thought about it

#

I'll try to explain it with an example

runic estuary Oct 28, 2022, 6:08 AM

#

storm mantle That's a good question, I'd never really thought about it

i am why proofs were invented 😭

storm mantle Oct 28, 2022, 6:08 AM

#

Let's say we have $\frac{1}{\frac{2}{3}}$

stone havenBOT Oct 28, 2022, 6:08 AM

#

Orthodox

runic estuary Oct 28, 2022, 6:08 AM

#

without them i would understand nothing

#

mhm

storm mantle Oct 28, 2022, 6:09 AM

#

Wait that explanation won't work

#

Hmm

#

So, division is the same as multiplying by 1/x

#

So y/x = y*1/x

#

Wait no that doesn't work either

storm mantle Oct 28, 2022, 6:10 AM

#

stone haven **Orthodox**

Okay, back to this

runic estuary Oct 28, 2022, 6:10 AM

#

oof this seems a lot harder to explain thsn to use

storm mantle Oct 28, 2022, 6:11 AM

#

Here you'll be doing 2/3 first, because the operation you're performing is 1/(2/3)

runic estuary Oct 28, 2022, 6:12 AM

#

mhm

storm mantle Oct 28, 2022, 6:12 AM

#

Division finds how many times the bottom goes into the top

storm mantle Oct 28, 2022, 6:12 AM

#

storm mantle Here you'll be doing 2/3 first, because the operation you're performing is 1/(2/...

Wait ignore this, this isn't necessary

storm mantle Oct 28, 2022, 6:13 AM

#

storm mantle Division finds how many times the bottom goes into the top

So we have this

#

And we're finding how many times 2/3 goes into 1

runic estuary Oct 28, 2022, 6:13 AM

#

yeh

storm mantle Oct 28, 2022, 6:14 AM

#

Since a smaller number will fit in more times, then by dividing 2 by 3 will allow it to fit into 1 more times

#

So the being in the bottom is allowing for the final answer to be larger

#

So just taking the three to the top will allow the equation to produce the same larger number

runic estuary Oct 28, 2022, 6:16 AM

#

ohhhhh

#

AHHHHH I GET IT NOW I THINK

storm mantle Oct 28, 2022, 6:17 AM

#

Honestly I explained that so poorly, I barely understand what I said

#

If you got it though that's good

runic estuary Oct 28, 2022, 6:17 AM

#

its just like

#

when u divide something by a decimal it gets bigger right

storm mantle Oct 28, 2022, 6:17 AM

#

Yeah

runic estuary Oct 28, 2022, 6:18 AM

#

so its the same with fractions and instead of doing all the silly math to get the same thing with more work youd just take the bottom and put it at the top

#

but your not taking the bottom and multiplying it by the top right?

storm mantle Oct 28, 2022, 6:18 AM

#

You would be taking the bottom and multiplying it by the top

#

So $\frac{2}{\frac{4}{3}}$ would be $\frac{2*3}{4}$

stone havenBOT Oct 28, 2022, 6:19 AM

#

Orthodox

runic estuary Oct 28, 2022, 6:21 AM

#

that is so helpful

#

another thing

#

if i have 2*sqrt(3)/2 the 2’s cancel out and the remainder is sqrt(3) right?

storm mantle Oct 28, 2022, 6:22 AM

#

Yep

#

Well, technically not remainder, just solution, but that's not really too important

#

Just definition thing

runic estuary Oct 28, 2022, 6:24 AM

#

wth i got the right answer just now but im confused cuz i got it wrong first and thrn i guessed

storm mantle Oct 28, 2022, 6:24 AM

#

What was it?

runic estuary Oct 28, 2022, 6:24 AM

#

so for cot of 13pi/6 i got 2/sqrt(3)/2

#

and then i did 4/sqrt(3) but it was wrong so i swapped it to sqrt(3) cuz thsts what i got for tangent and it was right

#

then i just did 1/sqrt(3) because cot is the reciprocal of tan

#

agh nvm i know why

#

i totally screwed up

storm mantle Oct 28, 2022, 6:27 AM

#

Nah, mathematicians make mistakes all the time

#

Like all the time

runic estuary Oct 28, 2022, 6:27 AM

#

well it was supposed to be

#

1/2/sqrt(3)/2

#

but i forgot the 1 at the top

storm mantle Oct 28, 2022, 6:28 AM

#

Ohh

runic estuary Oct 28, 2022, 6:28 AM

#

so it wouldve been sqrt(3) but i just did everything wrong

storm mantle Oct 28, 2022, 6:29 AM

#

I mean, the fact that you realized that means you're getting the hang of how these weird fractions work

#

You're doing well

runic estuary Oct 28, 2022, 6:29 AM

#

thank you

#

im gonna go to sleep now and figure out the rest in the morning

#

math is confusing stuff man im glad u find it fun

#Trig