Question

please help
\[{1 \over π}\int\limits_{-π}^{π}|\sin(x)|\cos(nx) dx\]

Answer 1

ok so the integrand is an even function right

Answer 2

doing fourier series?

Answer 3

yep

Answer 4

\[{1 \over π} ∫_0^π 2sin(x)cos(nx)dx\]

Answer 5

you are trying to find

\[a_n\] right?

Answer 6

and using a trig formulae..
2sin(x)cos(nx) = sin((1+n)x)+sin((1-n)x)

Answer 7

doing fourier series?

Answer 8

I think it should be
\[{1 \over π}\int\limits_{-π}^{π}|\sin( n x)|\cos(nx) dx\]

because

\[{1 \over π}\int\limits_{-π}^{π}|\sin(x)|\cos(nx) dx\]=0
by orthagonality

Answer 9

yeah i am trying to find the Fourier series of the absolute value of the sine wave
i already have \[a_0 = 4/π\] and \[b_n = 0\] even function

Answer 10

actually , you might not need to do all that since fourier series just respresentation using trig