- #1
zizou1089
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Homework Statement
Let f be the 2 periodic function defined on [−pi,pi ) by
f(x) = sin(x/3)
Find the Fourier coefficients of f.
Homework Equations
.5[cos(A-B)-cos(A+B)]=sinAsinB
The Attempt at a Solution
After much work using trigonometry and integration by parts I have deduced
(1/2pi) [(3/(1-3n))sin(((1-3n)/3)x) - (3/(1+3n))sin(((1+3n)/3)x)]
the trouble is when i put the limits [-pi,pi) into the equation I get 0 which is not the answer!
and the next part of the question states:
show for all x E (-pi,pi)
sin (x/3) = (((9)(3^.5))/pi)(((-1)^n)n)/(1-9n^2))