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## Main Question or Discussion Point

Today I had a maths exam with a question which was worded something like:

Write ##sin(3x-x_0)## as its Fourier representation. By doing a suitable integral or otherwise, find the possible values of its fourier coefficients. You may find the following useful:

##sin(\alpha-\beta) = sin(\alpha)cos(\beta) - cos(\alpha)sin(\beta)##.

5 marks.

I simply do not understand what was expected of me here. How is it even possible, or at least necessary, to write a basic sin function as a Fourier series? I thought the idea of the Fourier series was to write functions as a series of trig terms, so it makes no sense applying the concept to a function which is already trigonometric.

Does anyone have an alternative view on this?

Thanks.

Write ##sin(3x-x_0)## as its Fourier representation. By doing a suitable integral or otherwise, find the possible values of its fourier coefficients. You may find the following useful:

##sin(\alpha-\beta) = sin(\alpha)cos(\beta) - cos(\alpha)sin(\beta)##.

5 marks.

I simply do not understand what was expected of me here. How is it even possible, or at least necessary, to write a basic sin function as a Fourier series? I thought the idea of the Fourier series was to write functions as a series of trig terms, so it makes no sense applying the concept to a function which is already trigonometric.

Does anyone have an alternative view on this?

Thanks.