Chapter 6.3, Problem 100AYU

For what numbers $\theta$ is $f\left(\theta \right)=\csc \theta$ not defined?

To determine

To find: What numbers $\theta$ is $f\left(\theta \right)=\text{csc}\theta$ not defined.

Answer to Problem 100AYU

Solution:

$0,\pm \pi ,\pm 2\pi , \dots$

Explanation of Solution

Given:

$f\left(\theta \right)=\text{csc}\theta$

Calculation:

$f\left(\theta \right)=\text{csc}\theta =\frac{1}{\text{sin}\theta }$ is undefined when $\text{sin}\theta =0$.

Therefore $f\left(\theta \right)$ is not defined in $0,\pm \pi ,\pm 2\pi , \dots$.