# Math Help - TRIG: inverses

1. ## TRIG: inverses

Hello-
I am currently working on a problem and I don't completely understand how to get to the correct answer.
The problem is:
find exact value of:

sin-1[cos(-2pi over 3)]

(sorry, I haven't figured out how to manipulate text.)

I figure that it's -radical 3 over 2; -pi over 3. The book says it -pi over 6. I see that cos radical 3 over 2 is pi over 6, but sin radical 3 over 2 is pi over 3. (?)
Thanks.

2. from the unit circle (which you know well, correct?)

$\cos\left(-\frac{2\pi}{3}\right) = -\frac{1}{2}$

now ...

$\sin^{-1}\left(-\frac{1}{2}\right) = -\frac{\pi}{6}$