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Chapter 4: Problem 18

Find the period and amplitude. $$y=\frac{2}{3} \cos \frac{\pi x}{10}$$

Short Answer

Expert verified
The amplitude of the function \(y=\frac{2}{3}\cos(\frac{\pi x}{10})\) is \(\frac{2}{3}\), and the period is 20.

Step by step solution

01

Identify the amplitude

The amplitude is simply the absolute value of the constant A in the cosine function. In this case, from \(\frac{2}{3}\cos(\frac{\pi x}{10})\), the amplitude A is \(\frac{2}{3}\) because that is the value that multiplies the cosine function.
02

Identify the period

The period for a cosine or sine function is given by \(\frac{2\pi}{|B|}\), where B is the coefficient on x inside the cosine function. Here, B is \(\frac{\pi}{10}\), Therefore, the period is \(\frac{2\pi}{|\frac{\pi}{10}|} = 20\). The period is 20 because one complete cycle of the cosine wave occurs over a horizontal distance of 20 units.

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