# What is the period of f(theta)= sin 15 t - cos t ?

May 7, 2016

$2 \pi$.

#### Explanation:

The period for both sin kt and cos kt is $\frac{2 \pi}{k}$.

So, the separate periods for $\sin 15 t \mathmr{and} - \cos t a r e$(2pi)/15 and 2pi.

As $2 \pi$ is 15 X (2pi)/15,

$2 \pi$ is the period for the compounded oscillation of the sum.

$f \left(t + 2 \pi\right) = \sin \left(15 \left(t + 2 \pi\right)\right) - \cos \left(t + 2 \pi\right)$

= sin (15t+30pi))-cos(t+2pi)

$= \sin 15 t - \cos t$

= f(t).