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Identify the amplitude and period of the following function.

f(theta)=10 sin((pi theta)/(10))

Identify the amplitude and period of the following function. $\newline$ $f(\theta)=10 \sin \left(\frac{\pi \theta}{10}\right)$

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Find derivatives of sine and cosine functions

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Q. Identify the amplitude and period of the following function.

\newline

f(\theta)=10 \sin \left(\frac{\pi \theta}{10}\right)

Identify Function Form: Identify the general form of the function to determine amplitude and period. $\newline$ The function given is $f(\theta) = 10 \sin\left(\frac{\pi \theta}{10}\right)$ . This matches the general sine function form $A \sin(Bx)$ , where $A$ is the amplitude and the period is $\frac{2\pi}{B}$ .
Calculate Amplitude: Calculate the amplitude. The amplitude $A$ is the coefficient before the sine function, which is $10$ .
Calculate Period: Calculate the period. $\newline$ The period formula is $2\pi/B$ , where $B$ is the coefficient of $\theta$ inside the sine function. Here, $B = (\pi/10)$ . So, the period is $2\pi / (\pi/10) = 20$ .

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