A periodic function f(t), with a period of 2π, is represented as its Fourier series,\(f\left( t \right) = {a_0} + {\rm{\Sigma }}_{n = 1}^\infty \;{a_n}\cos nt + {\rm{\Sigma }}_{n = 1}^\infty \;{b_n}\sin nt\)If\(f\left( t \right) = \{ \begin{array}{*{20}{c}}{A\sin t,}&{0 \le t \le \pi }\\{0,}&{\pi < t < 2\pi }\end{array}\) ,the Fourier series coefficients a1 and b1 of f(t) are

• A. \({a_1} = \frac{A}{\pi };{b_1} = 0\)
• B. \({a_1} = \frac{A}{2};{b_1} = 0\)
• C. \({a_1} = 0;{b_1} = A/\pi\)
• D. \({a_1} = 0;{b_1} = \frac{A}{2}\)