Question

what is the period of $y = \csc x$?
a. $4\pi$, or $360^\circ$
b. $\frac{\pi}{2}$, or $180^\circ$
c. $2\pi$, or $360^\circ$
d. $\pi$, or $180^\circ$

Explanation:

Step1: Recall the definition of cosecant function

The cosecant function \( y = \csc x \) is the reciprocal of the sine function, i.e., \( \csc x=\frac{1}{\sin x} \).

Step2: Determine the period of sine function

The period of the sine function \( y = \sin x \) is \( 2\pi \) (or \( 360^\circ \)).

Step3: Analyze the period of cosecant function

Since the cosecant function is the reciprocal of the sine function, it will have the same period as the sine function because taking the reciprocal does not change the period of the function (it only affects the values where the function is defined, i.e., where \( \sin x
eq0 \)). So the period of \( y = \csc x \) is \( 2\pi \) (or \( 360^\circ \)).

Answer:

C. \( 2\pi \), or \( 360^\circ \)