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

1 Answer
Apr 8, 2016

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.