
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:
sin1[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. (?)
Please help.
Thanks.

from the unit circle (which you know well, correct?)
$\displaystyle \cos\left(\frac{2\pi}{3}\right) = \frac{1}{2}$
now ...
$\displaystyle \sin^{1}\left(\frac{1}{2}\right) = \frac{\pi}{6}$