Find the exact value, in radians of the expression cos^-1(sqrt3/2)

 

$$cos 30^0 =cos\frac{\pi}{6} = \sqrt3/2$$

cos is pos in the 1st and 4th quad

so

$$\\answer=2\pi n\pm\frac{\pi}{6}\qquad where\;\;n\in Z \\
$this means that n is an integer$$$

Edit

I've made a slight error here.

$$0\le cos^{-1}x \le \pi\\
$therefore the only answer is $
\dfrac{\pi}{6}$$

.