Question

cot(-8pi) find the exact value

Answer 1

Do you know what the cosine of \(8\pi\) is?

Answer 2

Nope! Honestly, I have no clue what's happening in class.

Answer 3

That's a problem D:

Answer 4

The cosine of 8pi is 1! :D that is what my calculator told me lol

Answer 5

Your calculator is quite right...though, if you're allowed to use a calculator, then what's the problem? Why not make it evaluate the cotangent for you? ^.^

Answer 6

Because it gives me a decimal and the answer is looking for a fraction. My calculator won't turn it into a fraction because it has a radical in the fraction.

Answer 7

Let me tell you a little secret...
\[\large \cot(x) = \frac1{\tan(x)}\]
So if you want the cotangent of something, just divide 1 by its tangent.

Go on, give Mr. Calculator another go :)

Answer 8

2.5E12. It won't make fractions :(

Answer 9

ooohh...
Okay, what's the tangent, then?

Answer 10

When I put in \[\cos (-8\pi)\div \sin(-8\pi)\]

Answer 11

I get the same answer

Answer 12

tangent of \(-8\pi\) what is it?

Answer 13

2.5E12

Answer 14

tangent.
tangent.
tangent.

:D

Answer 15

Oh mybad! Haha. 4E-13

Answer 16

No... what kind of calculator are you using? D:

Answer 17

TI-84

Answer 18

jeez XD

Why don't you just google tan(-8pi)

:D

Answer 19

I've tried :( it doesn't have anything for it! That's why I'm here lol. Would you happen to know tan(115pi)

Answer 20

:D

Answer 21

...yes.
But I'm not telling you :P

You'll need to figure it out for yourself... but I will help you :)

Trust me, google tan(-8pi) the answer is simpler than any fraction you could think of...

Answer 22

Oh my gosh...It's 0...so the answer is undefined because it would be 1/0!

Answer 23

Exactly :P

See? You CAN do it ^.^

Answer 24

You're smarter than your bloody TI-84 LOL

Answer 25

I have no clue why it's giving my crazy answers.

Answer 26

Don't trust it for now.
Want to know another secret that involves your precious tan(115pi) ? ^.^

Answer 27

Yes! I do enjoy a good secret!

Answer 28

Well then, now that we know that Google is a bit more reliable than Mr. TI-84, why don't you ask google the following:
tan(0pi)
tan(1pi)
tan(2pi)
tan(3pi)

I'll wait ^.^

Answer 29

They're all 0! So tan(xpi) will always be zero! Awesome to know! Why is that? If it is a lot to explain then don't worry about it; I'll just google it.

Answer 30

Correction:
tan(xpi) will be zero AS LONG as x is an integer.
Don't forget details, silly :P

Answer 31

But yes, you have made a good observation, and the explanation isn't long at all ^.^

Answer 32

And here's why:
\[\Large \sin(n\pi)= 0\]
for as long as n is an integer and...
\[\Large \cos(n\pi) = (-1)^n\]

That said, we have
\[\Large \tan(n\pi) = \frac{\sin(n\pi)}{\cos(n\pi)}= \frac0{(-1)^n}=0\]

Answer 33

I'm glad you didn't ask Google what tan(115pi) is, because somehow, at that point, Google becomes just as delusioned as TI-84

lawlz
^.^

Answer 34

Yeah! I typed it into google and it gave me something way off. Thanks a ton! You're a life savior!