need help

[Student]

Please solve complete question

 

[BigGlenntheHeavy]

Student's poser doesn't look that hard, however I don't understand exactly what he is aiming at, any takers?

$\displaystyle f(\theta) \ = \ sin(\theta)$

$\displaystyle f(\theta+2\pi) \ = \ sin(\theta+2\pi)$

$\displaystyle Hence, \ f(\theta) \ = \ f(\theta+2\pi), \ something \ on \ this \ order?$

 

[mmm4444bot]

Ted S is a taker, at another site where this exercise was posted, 1 hour ago. Ted writes:

you 1st extend F to be an odd function on [-? , ?] so that b_n = 2/? int over x in [0,?] of { F(x) sin nx dx} = 2 /? { 4 [(1/n²) sin(nx) - (x/n)cos(nx) ] - (1/n) cos (nx) } ..evaluate at ? and 0....you certainly can do that...? { n = 1,2,3,..} b_n sin (nx) = F(x)

So, perhaps the half-range sine series is just the Fourier series for the odd periodic extension of f(x).

I'm not sure.