Find the half range sine series of the function f(x) = x, when 0<x< ( frac{ pi}{2} ) and ( -x) when ( frac{ pi}{2} )<x< .

• A. ( frac{8}{ pi}[ frac{sinx}{1^{2}} sin frac{(3x)}{3^{2}} + sin frac{(5x)}{5^2} sin frac{(7x)}{7^{2}} + ] )
• B. ( frac{4}{ pi}[ frac{sinx}{1^{2}} + sin frac{(3x)}{3^{2}} + sin frac{(5x)}{5^2} + sin frac{(7x)}{7^{2}} + ] )
• C. ( frac{8}{ pi}[ frac{sinx}{1^{2}} + sin frac{(3x)}{3^{2}} + sin frac{(5x)}{5^2} + sin frac{(7x)}{7^{2}} + ] )
• D. ( frac{4}{ pi}[ frac{sinx}{1^{2}} sin frac{(3x)}{3^{2}} + sin frac{(5x)}{5^2} sin frac{(7x)}{7^{2}} + ] )