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A periodic function $\large{f(t)},$ with a period of 2$\pi$, is represented as its fourier series,

$\large{f(t)} = a_0 + \sum_{n=1}^{\infty }a_n cos nt + \sum_{n=1}^{\infty} b_n sin nt.$}$

If

$\large{f(t)} = \left\{\begin{matrix} Asint, & 0 \le t\le \pi\\ 0, & \pi < t < 2\pi \end{matrix}\right.$

the fourier series coefficients a_1 and b_1 of $\large{f(t)} $are

- $a_1 = \frac{A}{\pi}; b_1 = 0$
- $a_1 = \frac{A}{2}; b_1 = 0$
- $a_1 = 0;b_1 = \frac{A}{\pi}$
- $a_1 = 0;b_1 = \frac{A}{2}$

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