A question in my textbook asks me to determine if the function $f(x)=\cos(3x)+\sin(x)$ is periodic. I do not believe this to be the case as the arguments of sine and cosine are different and as such they cannot be written as a sinusoid. How can I determine for certain if the function is periodic or not?
Here's my attempt at answering my own question, please critique where possible.
A function is periodic if $f(x+p)=f(x) \therefore \cos(3(x+p)) + \sin(x+p) = \cos (3x) + \sin(x)$
Letting $x = 0$:
Where do I go from here? I know that this would hold when: sine is 0 and cosine is 1 OR when cosine is 0 and sine is 1. However how do I ascertain for which value of P this occurs?