if y = cos x, how many periods will there be between -5π and 9π?

Explanation:

Step1: Recall period of cosine function

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

Step2: Calculate length of interval

The length of the interval from $- 5\pi$ to $9\pi$ is $L=9\pi-(-5\pi)=14\pi$.

Step3: Find number of periods

Divide the length of the interval by the period. Let $n$ be the number of periods. Then $n=\frac{L}{T}=\frac{14\pi}{2\pi}=7$.

Answer:

7