Question

Find  a0 of the function \(f(x) = \sqrt{\frac{1-cosx}{2}}.\)

(a) \(\frac{4}{π} \)

(b) \(\frac{2}{π} \)

(c) \(\frac{π}{4} \)

(d) \(\frac{π}{2} \)

I had been asked this question by my college director while I was bunking the class.

This intriguing question originated from Fourier Series Expansions in chapter Fourier Series of Engineering Mathematics

Answer 1

Correct choice is (a) \(\frac{4}{π} \)

To explain: \(f(x) = \sqrt{\frac{1-cosx}{2}} = sin(\frac{x}{2}) \)

\(a_0 = \frac{1}{π} \int_0^{2π} sin(\frac{x}{2})dx \)

\( = \frac{1}{π} (-cos(\frac{x}{2}))^2 \)

\( = \frac{(-2)}{ π (-2)} \)

\( = \frac{4}{π} \)