how many periods of the function y = tan x are there between -8π and 2π?

Explanation:

Step1: Recall period of tangent function

The period of the function $y = \tan x$ is $\pi$.

Step2: Calculate number of periods

Find the length of the interval $[-8\pi,2\pi]$. The length $L=2\pi-(- 8\pi)=10\pi$. Since the period $T = \pi$, the number of periods $n=\frac{L}{T}=\frac{10\pi}{\pi}=10$.

Answer:

10