/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 40 Sketch the graph of the function... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 40

Sketch the graph of the function. (Include two full periods.) $$y=\frac{1}{4} \sin x$$

Short Answer

Expert verified
The graph of the function \(y=\frac{1}{4} \sin x\) is a sinusoidal wave that oscillates between \(1/4\) and \(-1/4\) and completes two full periods over the interval \(0\) to \(4\pi\).

Step by step solution

01

Identify the Basic Function

The basic function in this exercise is \(y=\sin x\), a standard sinusoidal function. A graph of \(y=\sin x\) completes one full period over the interval \(0\) to \(2\pi\)
02

Understand the Impact of the Constant Multiplier

The \(\frac{1}{4}\) multiplier in \(y=\frac{1}{4} \sin x\) affects the amplitude of the sinusoidal function. This will not change the period, but it will compress the graph vertically. The amplitude is \(\frac{1}{4}\), which means the highest and lowest points of the graph will only reach \(1/4\) and \(-1/4\) respectively.
03

Plot the Graph

Plot the sine function for the interval \(0\) to \(4\pi\) (to include two full periods) and compress it vertically to account for the \(\frac{1}{4}\) amplitude. The graph will oscillate between \(1/4\) and \(-1/4\) instead of \(1\) and \(-1\).

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