Question

For what numbers$\theta ,f\left(\theta \right)=cosec\left(\theta \right)$does not exist

Short answer

The function does not exist when$\theta$is integral multiple of$\pi$

Step-by-step solution

Given information

We are given$f\left(\theta \right)=\cos ec\left(\theta \right)$

Explanation

We have

$$\begin{gathered} f\left(\theta \right)=\cos ec\left(\theta \right) \\ f\left(\theta \right)=\frac{1}{\sin \left(\theta \right)} \end{gathered}$$

And the function does not exist when $\sin \left(\theta \right)=0$

This can happen only when

$\theta =n\pi$ that is theta is integral multiple of$\pi$