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Question 8 Find the $b_1$ terms of the Fourier series of the function below. $\begin{aligned} f(x) = \begin{cases} 5 & -\pi \le x \le 0\\ 0 & 0 < x \le \pi \end{cases} \end{aligned}$ Fourier Series $\begin{aligned} f(x) = a_0 + \sum_{n=1}^{\infty} a_n \cos(nx) + \sum_{n=1}^{\infty} b_n \sin(nx) \\\ f(x) = a_0 + a_1 \cos(x) + a_2 \cos(2x) + a_3 \cos(3x) + ... + b_1 \sin(x) + b_2 \sin(2x) + b_3 \sin(3x) + ... \end{aligned}$ $a_0 = \frac{1}{2\pi} \int_{-\pi}^{\pi} f(x) dx$ ; $a_n = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) \cos(nx) dx$ ; $b_n = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) \sin(nx) dx$ b? = [a] (use pi in place of ? or approximate your answer up to 3 decimal places)

          Question 8
Find the $b_1$ terms of the Fourier series of the function below.
$\begin{aligned} f(x) = \begin{cases} 5 & -\pi \le x \le 0\\ 0 & 0 < x \le \pi \end{cases} \end{aligned}$
Fourier Series
$\begin{aligned} f(x) = a_0 + \sum_{n=1}^{\infty} a_n \cos(nx) + \sum_{n=1}^{\infty} b_n \sin(nx) \\\ f(x) = a_0 + a_1 \cos(x) + a_2 \cos(2x) + a_3 \cos(3x) + ... + b_1 \sin(x) + b_2 \sin(2x) + b_3 \sin(3x) + ... \end{aligned}$ 
$a_0 = \frac{1}{2\pi} \int_{-\pi}^{\pi} f(x) dx$ ; $a_n = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) \cos(nx) dx$ ; $b_n = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) \sin(nx) dx$
b? = [a]
(use pi in place of ? or approximate your answer up to 3 decimal places)

Question 8
Find the b1 terms of the Fourier series of the function below.
f(x) = 5 -π≤ x ≤ 0
0 0 < x ≤π
Fourier Series
f(x) = a0 + ∑n=1^∞ an cos(nx) + ∑n=1^∞ bn sin(nx)
f(x) = a0 + a1 cos(x) + a2 cos(2x) + a3 cos(3x) + ... + b1 sin(x) + b2 sin(2x) + b3 sin(3x) + ...
a0 = (1)/(2π)∫-π^π f(x) dx ; an = (1)/(π)∫-π^π f(x) cos(nx) dx ; bn = (1)/(π)∫-π^π f(x) sin(nx) dx
b? = [a]
(use pi in place of ? or approximate your answer up to 3 decimal places)

Added by Francisca H.

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