question\ndetermine the period of the following graph.\nanswer attempt 1 out of 2

Answer:

$2\pi$

Explanation:

Step1: Recall the definition of period

The period of a periodic function is the horizontal length over which the function repeats.

Step2: Identify one full cycle

Looking at the graph, from (x = -\frac{\pi}{2}) to (x=\frac{3\pi}{2}), the function completes one full - cycle.

Step3: Calculate the length of the cycle

Use the formula (T=x_2 - x_1). Here (x_2=\frac{3\pi}{2}) and (x_1 =-\frac{\pi}{2}). Then (T=\frac{3\pi}{2}-\left(-\frac{\pi}{2}\right)=\frac{3\pi + \pi}{2}=2\pi).