Question

Confused on Arctan and such: http://prntscr.com/4cu103

Answer 1

Here's one way you can think about it.

Let \(x=\tan^{-1}\left(\sin\dfrac{\pi}{2}\right)\). Then taking the tangent of both sides, you have \(\tan x=\sin\dfrac{\pi}{2}=1\). What value of \(x\) gives a tangent of 1?

Answer 2

Tan is y/x on the unit circle, correct?

Answer 3

Yes

Answer 4

One sec, my unit circle isn't loading :/

Answer 5

π/4?

Answer 6

yep that's right

Answer 7

So is the answer π/4 or 1?

Answer 8

nvm, now that I think about it, I understand. The answer is π/4

Answer 9

You're solving for \(x\) in that equation I gave you.
\[\tan x=1~~\iff~~\tan\frac{\pi}{4}=1~~\Rightarrow~~x=\frac{\pi}{4}\]

Answer 10

Thanks, man/girl!