EasyCalculusca-105

Laplace Transform of Sine and Cosine

Problem

Return the Laplace transforms of sin(a*t) and cos(a*t) at s as [L_sin, L_cos].

L{sin(a t)} = a / (s^2 + a^2) and L{cos(a t)} = s / (s^2 + a^2). Assume s > 0; a may be zero.

Hint

Both transforms share the denominator s^2 + a^2.

case 1

in: [1,1]

expected: [0.5,0.5]

case 2

in: [2,1]

expected: [0.4,0.2]

case 3

in: [0,1]

expected: [0,1]

case 4

in: [3,4]

expected: [0.12,0.16]

case 5

in: [1,2]

expected: [0.2,0.4]

Starter codePython

def laplace_sin_cos(a, s):
    # Return [L_sin, L_cos]
    # Your code here
    pass

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