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Chapter 4: Problem 14

Find the period and amplitude. $$y=\frac{1}{5} \sin 6 x$$

Short Answer

Expert verified
The amplitude of \(y=\frac{1}{5} \sin 6x\) is 0.2 and the period is \(\frac{\pi}{3}\).

Step by step solution

01

Identify the amplitude

The coefficient of the sine term in the equation gives the amplitude of the function. In this problem, it's \(\frac{1}{5}\), so the amplitude is \(\frac{1}{5}\) or 0.2.
02

Identify the coefficient of x

The coefficient of \(x\) in the sine function determines the function's period. Here, the coefficient is 6.
03

Calculate the period

The period of a sine function can be found by dividing \(2\pi\) by the absolute value of the coefficient of \(x\). In this case, the period is given by \(T=\frac{2\pi}{|6|} = \frac{\pi}{3}\)

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