what is the period of y = csc(x)?\no $pi$\no $2pi$\no $3pi$\no $4pi$

Explanation:

Step1: Recall the definition of cosecant function

The cosecant function is defined as $y = \csc(x)=\frac{1}{\sin(x)}$.

Step2: Recall the period of sine function

The period of $y = \sin(x)$ is $2\pi$. That is, $\sin(x)=\sin(x + 2\pi)$ for all $x$ in the domain of $\sin(x)$.

Step3: Determine the period of cosecant function

Since $\csc(x)=\frac{1}{\sin(x)}$ and $\sin(x)=\sin(x + 2\pi)$, then $\csc(x)=\csc(x + 2\pi)$ for all $x$ in the domain of $\csc(x)$ (where $\sin(x)\neq0$). So the period of $y=\csc(x)$ is the same as the period of $y = \sin(x)$, which is $2\pi$.

Answer:

$2\pi$ (corresponding to the second option)