What is the Fourierseries of the following equation?
#f(x)=|sin(x)|#
1 Answer
Explanation:
graph{y = abs(sin x) [-10, 10, -1, 3]}
The function has period
#{(a_0 = 1/L int_0^(2L)f(x )dx),(a_n = 1/L int_0^(2L)f(x )cos((npix )/L)dx), (f(x)=1/2a_0+sum_(n=1)^infty a_n cos((npi x)/L)),(2L = pi):} #
Using this ID:
#2\sin \theta \cos \varphi =\sin(\theta +\varphi )+\sin(\theta -\varphi )#
From the definition:
Looks like this for first few terms:
graph{(y - 2/pi + 4/pi ( ( cos (2x) )/3+ ( cos (4 x) ) / 15 + ( cos(6x) ) / 35 ))(y - |sin x|) = 0 [0, 5, -0.1 , 1.25]}