Question

The period of the funtion
$f(\theta )=\sin (\frac{\theta }{3})+\cos (\frac{\theta }{2})$ is

• A. $3\pi$
• B. $6\pi$
• C. $9\pi$
• D. $12\pi$

Answer 1

The correct option is D $12\pi$

$f\left(x\right)=\sin \frac{\theta }{3}+\cos \frac{\theta }{2}$, where $\sin \frac{\theta }{3}\to period=6\pi and\cos \frac{\theta }{2}\to Period=4\pi$
$\therefore$ period of $f\left(x\right)=LCMof(6\pi ,4\pi )=12\pi$