# What is the frequency of #f(theta)= sin 18 t - cos 42 t #?

##### 1 Answer

Period

See the oscillation in the graph, for tthe compounded wave, within one period

#### Explanation:

graph{sin (18x)-cos (12x) [-0.525, 0.525 -2.5, 2.5]} The period of both sin kt and cos kt is

Here, the separate periods of the two terms are

The period ( least possible ) P, for the compounded oscillation, is

given by

for least possible ( positive ) integer multiples L and M such that

For

Note that P/2 is not the period, so that P is the least possible value.

See how it works.

Check by back substiution P/2, instead of P, for least P.

The frequency