Question

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

Answer 1

`2pi`

Explanation:

The period for `sin kt = 2pi/k`.

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

So, this is the period for the compounded oscillation.
`f(t)=sin 2t-sin 5t`.

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