# Thread: Period of the sum of two cosines

1. ## Period of the sum of two cosines

Hello,

I remember that if I sum two cosine waves the period of the resulting function will be extended. How do I find this new period? I also remember that if the ratio of the periods satisfies a condition then the period never repeats. I do not remember what the condition is. Or maybe it should be a multiplication and not a sum... Can someone remind me about this?

Thanks a lot.

2. Hello,

Originally Posted by sjcomp
Hello,

I remember that if I sum two cosine waves the period of the resulting function will be extended. How do I find this new period? I also remember that if the ratio of the periods satisfies a condition then the period never repeats. I do not remember what the condition is. Or maybe it should be a multiplication and not a sum... Can someone remind me about this?

Thanks a lot.
In general, the period would be the least common multiple of the two periods you have been given.

For example : period pi/2 and period pi/3.

2*pi/2=pi
3*pi/2=3pi/2
4*pi/2=2pi
.
.
.
----------
2*pi/3=2pi/3
3*pi/3=pi
4*pi/3=4pi/3
.
.
.

Period is pi

If you give an example, I think I'll be able to explain better

3. Thanks, Moo. I see it's the same method as your reply to my other question Do you know anything about my second question if there is a relationship between the summed periods that would not result in a common multiple?

Thanks.