# Question #a6825

Feb 17, 2018

See below

#### Explanation:

Instead of $\cos \left(2 x\right) = 0$, think of the equation as $\cos \left(\theta\right) = 0$, where $\theta = 2 x$

Since $\cos \theta = 0$ at $\theta = \frac{\pi}{2}$ and $\theta = \frac{3 \pi}{2}$, then by substitution,

$\cos \left(2 x\right) = 0$ at $2 x = \frac{\pi}{2}$ and $2 x = \frac{3 \pi}{2}$

Solve each equation separately

$2 x = \frac{\pi}{2}$
$x = \frac{\pi}{2} \times \frac{1}{2}$
$x = \frac{\pi}{4}$

$2 x = \frac{3 \pi}{2}$
$x = \frac{3 \pi}{2} \times \frac{1}{2}$
$x = \frac{3 \pi}{4}$