Fourier Cosine Coefficient

Problem

For f(x) = x on the interval (0, pi), the Fourier cosine coefficients are a_n = (2/pi) * integral from 0 to pi of x*cos(n*x) dx.

Integration by parts gives a_n = 2 * ((-1)^n - 1) / (pi * n^2). Return a_n for a given positive integer n, using 3.141592653589793 for pi.

Hint

Odd coefficients vanish because the boundary term alternates sign: cos(n*pi) - 1.

case 1

in: [1]

expected: -1.2732395447351628

case 2

in: [2]

expected: 0

case 3

in: [3]

expected: -0.1414710605261292

case 4

in: [4]

expected: 0

case 5

in: [5]

expected: -0.05092958178940651

Starter codePython

def fourier_cosine_x(n):
    # Your code here
    pass

5 test cases · run your code against them in the editor