how many periods of the function y = sec x are there between -π/2 and 3π/2?

Answer:

1

Explanation:

Step1: Recall period of secant function

The period of $y = \sec x$ is $2\pi$.

Step2: Calculate length of given interval

The length of the interval from $-\frac{\pi}{2}$ to $\frac{3\pi}{2}$ is $\frac{3\pi}{2}-\left(-\frac{\pi}{2}\right)=\frac{3\pi + \pi}{2}=2\pi$.

Step3: Determine number of periods

Since the length of the interval is $2\pi$ and the period of $y=\sec x$ is $2\pi$, the number of periods is $\frac{2\pi}{2\pi}=1$.