# Question #7d614

Dec 29, 2016

The period is $= 4 \pi$

#### Explanation:

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

The period of $\sin \left(\frac{x}{2}\right)$ is $= \frac{2}{\frac{1}{2}} \pi = 4 \pi$

The period of $\cos \left(\frac{x}{2}\right)$ is $= \frac{2}{\frac{1}{2}} \pi = 4 \pi$

$4 = 2 \cdot 2$

$4 = 2 \cdot 2$

LCM $\left(4 , 4\right) = 4$

The LCM of $4 \pi$ and $4 \pi$ is $= 4 \pi$

The period is $T = 4 \pi$

graph{sin(x/2)-cos(x/2) [-12.76, 19.27, -7.66, 8.36]}