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Chapter 4: Problem 9

Find the period and amplitude. $$y=\frac{1}{2} \sin \frac{\pi x}{3}$$

Short Answer

Expert verified
Amplitude is 0.5 and Period is 6.

Step by step solution

01

Identify the amplitude.

The amplitude of the function is the absolute value of the coefficient of the sine function. Here, the amplitude 'A' is \(|1/2|\), which equals to 0.5.
02

Identify the coefficient of x inside the sine function.

The coefficient 'B' of 'x' inside the sine function is \(\pi/3\).
03

Calculate the period.

The period of the function is found by dividing \(2\pi\) by the absolute value of the coefficient of 'x'. Hence, the period of the function is \(2\pi / |\pi/3|\), which simplifies to 6.

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