Question

The period of the function $f\left(\theta \right)=4+4\sin 3\theta -3\sin \theta$ is:

• A. $\frac{2\mathrm{\pi }}{3}$
• B. $\frac{\mathrm{\pi }}{3}$
• C. $\frac{\mathrm{\pi }}{2}$
• D. $\mathrm{\pi }$

Answer 1

The correct option is A

$\frac{2\mathrm{\pi }}{3}$

Explanation for the correct option:

Compute the period of the given function.

$f\left(\theta \right)=4+4\sin 3\theta -3\sin \theta$

$=4–(3\sin \theta –4\sin 3\theta )$

$=4–\sin 3\theta$

$f\left(\theta +\frac{2\pi }{3}\right)=4–\sin \left[3\left(\theta +\frac{2\pi }{3}\right)\right]$

$=4-\sin (3\theta +2\pi )=4-\sin 3\theta$

Thus, the period of $f\left(\theta \right)$ is $\frac{2\pi }{3}$.

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