What is the period of f(t)=sin(t/3)+ cos( (2t)/5) ?

Jun 7, 2017

The period is $= 30 \pi$

Explanation:

The period of the sum of 2 periodic functions is the LCM of their periods.

The period of $\sin \left(\frac{t}{3}\right)$ is ${T}_{1} = \frac{2 \pi}{\frac{1}{3}} = 6 \pi$

The period of $\sin \left(\frac{2}{5} t\right)$ is ${T}_{1} = \frac{2 \pi}{\frac{2}{5}} = 5 \pi$

The LCM of $\left(6 \pi\right)$ and $\left(5 \pi\right)$ is $= \left(30 \pi\right)$

So,

The period is $= 30 \pi$