Periods of Powers of Trigonometric Functions

AI Thread Summary
To determine the period of a function like f(x) = a*sin(b*x)^2 + c*cos(d*x)^2 + e*sin(f*x) + g*cos(h*x), one can utilize trigonometric identities, particularly the half-angle identities for sin^2(x) and cos^2(x). The challenge arises from the presence of squared terms, which complicates the periodicity analysis. A suggested approach is to substitute values for the constants and graph the function to observe its behavior. Understanding the individual periods of the sine and cosine components is crucial, as they can be combined to find the overall period. Utilizing these strategies can lead to a clearer method for analyzing arbitrary periodic sums.
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Homework Statement


Is there a way to determine the period of a function like f(x) = a*sin(b*x)^2 + c*cos(d*x)^2 + e*sin(f*x) + g*cos(h*x)?


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The Attempt at a Solution


I know how to find the periods of sines, cosines, and arbitrary sums of the two, but the introduction of exponents has me at a complete loss. Please don't show me how; just point me in the general direction.
 
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I only have a basic knowledge of trigonometric functions, but without any other indicator of how to approach this I'd put in arbitrary values for the constants a, b, c, d, e, f, g, and h, graph the function, and it seems like you'd be able to derive a method of finding arbitrary periodic sums. Just a thought..
 
Use trig identities for sin2 x and cos2 x.
 
I forgot all about the half-angle identities... Thank you
 
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