1. Tardigrade
  2. Question
  3. Mathematics
  4. The period of f(x)= cos ((x/3))+ sin ((x/2)) is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The period of $f(x)=\cos \left(\frac{x}{3}\right)+\sin \left(\frac{x}{2}\right)$ is

EAMCETEAMCET 2013

Solution:

Given, $f(x)=\cos \left(\frac{x}{3}\right)+\sin \left(\frac{x}{2}\right)$
Period of $\cos x$ and $\sin x$ are $2 \pi$.
$\therefore $ Period of $f(x)=$ Period of
$\left[\cos \frac{x}{3}+\sin \frac{x}{2}\right]$
=Period of $\cos \frac{x}{3}+$ Period of $\sin \frac{x}{2}$
$=\frac{2 \pi}{\left(\frac{1}{3}\right)}+\frac{2 \pi}{\left(\frac{1}{2}\right)}=\frac{6 \pi}{1}+\frac{4 \pi}{1}$
$=\frac{\text { LCM of }(6 \pi, 4 \pi)}{\text { LCM of }(1,1)}=\frac{12 \pi}{1}=12 \pi$