how many periods of the function y = sin x are there between -10π ≤ 0 ≤ 6π ?

Explanation:

Step1: Recall period of sine function

The period of the function $y = \sin x$ is $T = 2\pi$.

Step2: Calculate length of the interval

The length of the interval from $- 10\pi$ to $6\pi$ is $L=6\pi-(-10\pi)=16\pi$.

Step3: Divide interval length by period

The number of periods $n=\frac{L}{T}=\frac{16\pi}{2\pi}=8$.

Answer:

8