What is the fundamental period of 3cos(1.3PiN) - 4sin(0.5piN + 0.5Pi)?

[mbanghart]

Hi all,

First post here for me.

1. Problem Statement

Find the fundamental period of:
3cos(1.3PiN) - 4sin(0.5piN +0.5Pi)

2. Relevant equations:
T = 2PI / w

3. My attempt:
Not sure how to proceed. By themselves the fundamentals period would be:
3cos(1.3PiN)

w = 1.3Pi thus T = 2/1.3

4sin(0.5piN +0.5Pi)

w = 0.5pi thus T = 2/0.5

However, I need to combine the equation somehow? It has been a long time since I had calculus and I do not remember.

Thanks

 

[fresh_42]

Looks like round about $8$:
https://www.wolframalpha.com/input/?i=3cos(1.3+*+pi+*+N)+-+4sin(0.5+*pi+*+N++0.5+*pi)
It is always a good idea to start with what you have, in this case the function and the definition of fundamental period!

You could try to find zeros of the function as well as of its derivative and compare the second derivative at these points. Note that the function satisfies $f(-x)=f(x)$.