# Finding the period of 2 multiplied trig functions

## Main Question or Discussion Point

I am trying the period of 2 cosine functions that are multiplied with each other, but I am blanking out on how to find them.

For example, given a function like:

x(t) = cos(10*pi*t)cos(20*pi*t)

I know it has something to do with the frequency of both functions (10*pi & 20*pi), but I cannot remember it and I cannot find it anywhere else. If someone can give me the first part or two of trying to find it, I am hoping it will click.

Any help will be greatly appreciated!

Nick

berkeman
Mentor
I am trying the period of 2 cosine functions that are multiplied with each other, but I am blanking out on how to find them.

For example, given a function like:

x(t) = cos(10*pi*t)cos(20*pi*t)

I know it has something to do with the frequency of both functions (10*pi & 20*pi), but I cannot remember it and I cannot find it anywhere else. If someone can give me the first part or two of trying to find it, I am hoping it will click.

Any help will be greatly appreciated!

Nick

http://www.themathpage.com/atrig/trigonometric-identities.htm

(BTW, I found it using a Google search on: cos a cos b)

Stephen Tashi
I know it has something to do with the frequency of both functions
You must use trig to understand the frequency of each function, but once you do that getting the answer doesn't depend on the fact that you are dealing with trig functions. There should be a method that works for any type of periodic function. Try taking the least common multiple of the two frequencies.

When you get into problems like finding the frequency of sin(10 pi t + 6) cos( 20 pi t + 4), trig might be useful, but I wonder if it is necessary. For example: Given the period of f(x) is 3 and the period of g(x) is 9, what is the period of f(x-7)g(x+4) ? Does this problem have a definite answer? It's too late at night for me to think about it!