Is this a finite fourier series?

so i have just been given a function in terms of cos and sin, and using eulers equations ive come out with what i believe to be a finite fourier series but not totally sure - would 1/2(sin(5t)+sin(3t)) be considered a finite fourier series?
thanks

Yes.

thankyou for your quick reply - may i ask why it is? we didnt really cover finite series

thankyou for your quick reply - may i ask why it is? we didnt really cover finite series

EDIT: Fourier series of a trig function would be finite, as it's kinda like the principle of using the Taylor series to approximate a polynomial - most terms turn out to be 0 and you end up with what you started, maybe just written differently, but you end up with finite terms.

This isn't really true. It's true for a sum of sin/cos times that are all periodic with the same period as your Fourier series, but it won't be true for, say $\sin(\sqrt{2} x)$ (between 0 and 2pi), and I'm pretty (very) sure it's not true for something like $\dfrac{1}{1+\sin^2 x}$ between 0 and 2pi, although I can't be bothered to do the actual math to check.