for which value of $\theta$ is $csc(\theta)$ undefined?\n0\n$\frac{pi}{2}$\n$\frac{3pi}{2}$\n$\frac{7pi}{2}$

Explanation:

Step1: Recall the definition of cosecant

The cosecant function is defined as $\csc(\theta)=\frac{1}{\sin(\theta)}$. It is undefined when $\sin(\theta) = 0$.

Step2: Evaluate $\sin(\theta)$ for each option

• For $\theta = 0$, $\sin(0)=0$.
• For $\theta=\frac{\pi}{2}$, $\sin(\frac{\pi}{2}) = 1$.
• For $\theta=\frac{3\pi}{2}$, $\sin(\frac{3\pi}{2})=- 1$.
• For $\theta=\frac{7\pi}{2}$, $\sin(\frac{7\pi}{2})=\sin(4\pi-\frac{\pi}{2})=-\sin(\frac{\pi}{2})=-1$.

Answer:

$0$