Given:
The function is given:
[tex]f(\theta)=13\tan (\frac{\theta}{4})[/tex]
To find:
The period of the function.
Solution:
It is known that the period of the function A tan (nx) is pi/n.
So, the period of the given function is:
[tex]\begin{gathered} \text{Period}=\frac{\pi}{\frac{1}{4}} \\ =4\pi \end{gathered}[/tex]
Thus, the period of the given function is 4pi.
Thus, option D is correct.
