Question

Find the fourier sine transform of F(x) = -x when x<c and (π – x) when x>c and 0≤c≤π.

(a) \(\frac{π}{c} cos(pc) \)

(b) \(\frac{π}{p} cos(pc) \)

(c) \(\frac{π}{c} cos(pπ) \)

(d) \(p \frac{π}{c} cos(pc) \)

I have been asked this question during an online exam.

Enquiry is from Fourier Transform and Convolution topic in chapter Fourier Integral, Fourier Transforms and Integral Transforms of Engineering Mathematics

Answer 1

The correct choice is (b) \(\frac{π}{p} cos(pc) \)

Explanation: \(fs(p) = – \int_0^c x sin(px)dx + \int_c^π (π-x)  sin(px)dx \)

\( = \frac{π}{p} cos(pc). \)