Question

The Fourier series for the function f (x) = sin^2x is ______________

(a) 0.5 + 0.5 sin 2x

(b) 0.5 – 0.5 sin 2x

(c) 0.5 + 0.5 cos 2x

(d) 0.5 – 0.5 cos 2x

The question was asked during an interview.

The question is from Fourier Analysis topic in portion Fourier Analysis on Complex Spaces of Signals and Systems

Answer 1

Correct answer is (d) 0.5 – 0.5 cos 2x

To explain I would say: f(x) = sin^2x

Now, f(x) = sin^2x = \(\frac{1-cos⁡2x}{2}\)

= 0.5 – 0.5 cos 2x.