# What is the period of f(theta)= sin 2 t - cos 5 t ?

Apr 8, 2016

$2 \pi$

#### Explanation:

The period for $\sin k t = 2 \frac{\pi}{k}$.

The separate periods for sin 2t and sin 5t are $\pi$ and the smaller $2 \frac{\pi}{5}$. Match with suitable integer multiples m and n such that $m = 2 \frac{n}{5}$. .
The least common multiple period is $2 \pi$, for m=2 and n=5. .

So, this is the period for the compounded oscillation.
$f \left(t\right) = \sin 2 t - \sin 5 t$.

The laast value of P for which f(t+P)=f(t) is $2 \pi$.