# How do you find the period of sin3x+cos7x?

May 5, 2017

The period is $= 2 \pi$

#### Explanation:

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

The period of $\sin 3 x$ is ${T}_{1} = \frac{2}{3} \pi = \frac{14}{21} \pi$

The period of $\cos 7 x$ is ${T}_{2} = \frac{2}{7} \pi = \frac{6}{21} \pi$

The LCM of $\frac{14}{21} \pi$ and $\frac{6}{21} \pi$ is $= \frac{42}{21} \pi$

Therefore,

the period is $T = 2 \pi$