# What is the domain and range of cos^-1 [sqrt(1/4 - x^2)]??

Oct 31, 2016

Domain: $- \frac{1}{2} \le x \le \frac{1}{2}$ Range: $\frac{\pi}{3} \le y \le \frac{\pi}{2}$

#### Explanation:

Find the domain,

$\frac{1}{4} - {x}^{2} \ge 0$

$\frac{1}{4} - {x}^{2} \ge 0$

${x}^{2} \le \frac{1}{4}$

$- \frac{1}{2} \le x \le \frac{1}{2}$

This makes the argument of the inverse cosine function vary from

${\cos}^{-} 1 \left(0\right) \to {\cos}^{-} 1 \left(\frac{1}{2}\right)$

$\frac{\pi}{2} \to \frac{\pi}{3}$