Question

Write the seven terms of the Fourier series for a function with period 2π and with the coefficients a0=6.5, a1=-4.2, a2=2.1, a3=3.1, b1=8.5, b2=-4.3, b3=3.8?

Answer 1

`f(x) = 3.25 - 4.2 cos x + 8.5 sin x + 2.1 cos 2x - 4.3 sin 2x + 3.1 cos 3x + 3.8 sin 3x`

Explanation:

For period `2 pi`, `f(x) = 1/2a_0+sum_(n=1)^oo a_ncos(nx) + sum_(n=1)^oo b_nsin(nx)`

`implies f(x) = 3.25 - 4.2 cos x + 8.5 sin x + 2.1 cos 2x - 4.3 sin 2x + 3.1 cos 3x + 3.8 sin 3x`