Question

−\frac{\pi}{2}<\theta<\frac{\pi}{2}. find the value of \theta in radians.
\tan(\theta)=0
write your answer in simplified, rationalized form. do not round.
\theta =

Explanation:

Step1: Recall tangent function property

The tangent function $y = \tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}$. We know that $\tan(\theta)=0$ when $\sin(\theta)=0$ and $\cos(\theta)
eq0$.

Step2: Find $\theta$ in given range

The general solutions of $\sin(\theta)=0$ are $\theta = k\pi$, where $k\in\mathbb{Z}$. Given $-\frac{\pi}{2}<\theta<\frac{\pi}{2}$, when $k = 0$, $\theta=0$ satisfies both $\tan(\theta)=0$ and the given range.

Answer:

$0$