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Chapter 4: Problem 5

Find the period and amplitude. $$y=2 \sin 5 x$$

Short Answer

Expert verified
The amplitude of the function \(y=2 \sin 5x\) is 2 and the period of the function is \(\frac{2\pi}{5}\).

Step by step solution

01

Find the Amplitude

The amplitude of a sine function is given by the absolute value of the coefficient A of the sine function. Look at the equation \(y=2 \sin 5x\), the coefficient of the \(\sin\) function is 2, so the amplitude of the function is \(|2|\) i.e., 2.
02

Find the Period

The period of a basic sine function is \(2\pi\). For the function \(y = A \sin(Bx)\), the period changes and is given by \( \frac{2\pi}{|B|}\), where B is the coefficient of x in the sine function. In the given equation \(y=2 \sin 5x\), B = 5. Therefore, the period of the function is \( \frac{2\pi}{|5|}\) i.e., \(\frac{2\pi}{5}\).

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