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Chapter 4: Problem 17

Find the period and amplitude. $$y=\frac{1}{4} \sin 2 \pi x$$

Short Answer

Expert verified
The amplitude of the function is \(\frac{1}{4}\) and the period is 1.

Step by step solution

01

Identify the Amplitude

The amplitude of a trigonometric function is the absolute value of the coefficient of the sine or cosine term. In this case, the amplitude \(A\) is \(| \frac{1}{4} |\), which is \(\frac{1}{4}\). So the amplitude is \(\frac{1}{4}\).
02

Identify the 'B' value

The coefficient of 'x' in the sine term is referred to as the 'B' value in the equation and it aids in finding the period of the function. Here, \(B\) = \(2\pi\).
03

Calculate the Period

The period of the function is calculated by dividing \(2\pi\) by the absolute value of B. So, the period \(T = \frac{2\pi}{|B|} = \frac{2\pi}{2\pi} = 1\). Therefore, the period of the function is 1.

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