# How do you find the period of H = 10 + 4 sin (pi/6)(t)?

May 1, 2016

12.

#### Explanation:

The period of sin kt is $\frac{2 \pi}{k}$ and so is the period of a + b sin kt.

Here, $k = \frac{\pi}{6} , \frac{2 \pi}{k} = 12$.

Check:
$H \left(t + 12\right) = 10 + 4 \sin \left(\left(\frac{\pi}{6}\right) \left(t + 12\right)\right)$
$= 10 + 4 \sin \left(\left(\frac{\pi}{6}\right) t + 2 \pi\right)$
$= 10 + 4 \sin \left(\frac{\pi}{6}\right) t$
$= H \left(t\right)$