Help with Trig function Periods

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The discussion focuses on the challenges of finding the fundamental periods of complex trigonometric functions, particularly when they involve powers or different natural frequencies. The user initially struggles with functions like 3Cos3x + 2Cos2x, Cos2x, and sin2x, despite being comfortable with simpler forms. They attempt to use double and half angle formulas but find limited success. Ultimately, the user reports a breakthrough in solving the problems just after posting for help. The discussion highlights the common difficulties in mastering trigonometric function periods and the potential for sudden clarity in problem-solving.
Steveh15
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Hello!

I'm having some trouble with finding the fundamental period of the slightly more complex trig functions. I think it's pretty simple stuff but I can't seem to crack it and I really need to get this bit sorted before I can move on with Fourier Expansions.

I can do the more simple stuff, like finding the period of Asin(wx) and ASin(wx) + BCos(wx).

The ones I can't do are things like when the trig functions are raised to a power or when two are added together which have different natural frequencies.

The specific ones in my problem sheet are.

3Cos3x + 2Cos2x
Cos2x
sin2x

My attempt at an answer? Not far really. I've been messing around with the double and half angle formulaes as well as addition formulaes trying to reduce them to a form I can work with but I'm not getting far.

If someone could explain how these are meant to be done or point me in the direction of some resources that would be great. My textbooks have let me down on this one and it's driving me crazy!

Thanks a lot
Steve
 
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I've just solved all of these oddly enough. The moment I hit post I had a brainwave and got it. Thanks very much for any help that might have arrived though :).
 

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