Answer:
The period of the tangent function is π because the graph repeats itself on intervals of kπ where k is a constant.
The function of the tan function is given below as
[tex]y=\tan x[/tex]
The graph of the function below is given as
To determine the period between the
[tex]\begin{gathered} -4\pi\text{ and }\pi \\ =\frac{\pi-(-4\pi)}{\pi} \\ =\frac{\pi+4\pi}{\pi} \\ =\frac{5\pi}{\pi} \\ =5 \end{gathered}[/tex]
Hence,
The number of periods of the function y = tanx between -4π and π is 5
