Question

what is the period of the parent cosecant graph?
answer
○ $\pi$ ○ $2\pi$
○ $\frac{\pi}{2}$ ○ $\frac{\pi}{b}$

Explanation:

Step1: Recall Cosecant Period

The parent cosecant function is \( y = \csc(x) \), which is the reciprocal of \( \sin(x) \). The period of \( \sin(x) \) is \( 2\pi \), and since cosecant has the same period as sine (as it's a reciprocal transformation that doesn't change the period), the period of \( \csc(x) \) is \( 2\pi \).

Step2: Match with Options

Among the options (\( \pi \), \( \frac{\pi}{2} \), \( 2\pi \), \( \frac{\pi}{b} \)), \( 2\pi \) is the correct period for the parent cosecant graph.

Answer:

\( 2\pi \) (the option with \( 2\pi \))