# How do you simplify tan(arccos(x/3))?

Aug 2, 2016

$\frac{\sqrt{9 - {x}^{2}}}{x} , - 3 \le x \le 3$.

#### Explanation:

Let $a = \arccos \left(\frac{x}{3}\right) \in Q 1 \mathmr{and} Q 2 , - 1 \le \frac{x}{3} \le 1$, and so, $- 3 \le x \le 3$

Then, $\cos a = \frac{x}{3} , \sin a = \sqrt{1 - {\cos}^{2} a} = \sqrt{1 - {x}^{2} / 9}$,

Now, the given expression is

$\tan a = \sin \frac{a}{\cos} a$

$= \frac{\sqrt{9 - {x}^{2}}}{x} ,$