Question

The period of $\sin \left(h\frac{x}{2}\right)$ is

• A. $2\pi i$
• B. $cot\left(hx\right)$
• C. $4\pi i$
• D. $cothx$

Answer 1

The correct option is C

$4\pi i$

Explanation for the correct option:

Compute the period of the given function.

We know that the period of $\sin \left(hx\right)$ is $2\pi i$,

So, the period of sine hyperbolic for half-angle, i.e., $\sin \left(h\frac{x}{2}\right)$ $=2\left(2\mathrm{\pi i}\right)=4\mathrm{\pi i}$

Thus, the period of $\sin \left(h\frac{x}{2}\right)$ is $4\mathrm{\pi i}$.

Hence, option $\left(\mathrm{C}\right)$ is the correct answer.