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Chapter 4: Problem 8

Find the period and amplitude. $$y=-3 \sin \frac{x}{3}$$

Short Answer

Expert verified
The amplitude of the function is 3 and the period is \(3\pi\).

Step by step solution

01

Find the Amplitude

Looking at the function \(y=-3 \sin \frac{x}{3}\), we see that the coefficient of the sine function is -3. The amplitude is the absolute value of this coefficient. Therefore, the amplitude of this function is |-3| = 3.
02

Find the Period

In the given function, we can observe that inside the sine function, there is \(\frac{x}{3}\). Since the period of a sine function is given by the reciprocal of the coefficient of \(x\) inside the function, we can determine the period by taking the reciprocal of \(\frac{1}{3}\), which provides us with the period = 3 \(\pi\).

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