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Chapter 4: Problem 2

Determine the amplitude of each function. Then graph the function and \(y=\sin x\) in the same rectangular coordinate system for \(0 \leq x \leq 2 \pi\). $$y=5 \sin x$$

Short Answer

Expert verified
The amplitude of the function \(y=5 \sin x\) is \(5\). Its graph shows a sine curve peaking at \(5\) and troughing at \(-5\), whereas the sine function \(y=\sin x\) has an amplitude of \(1\), with its graph peaking at \(1\) and troughing at \(-1\).

Step by step solution

01

Determine the amplitude of the function

The amplitude of the function \(y=5 \sin x\) is given by the absolute value of the coefficient of the sine function. In this case, it is \(5\).
02

Graph the function y=5 sin x

Using a graphing tool, you can plot the function \(y=5 \sin x\) along with its corresponding x-values from 0 to \(2 \pi\). It will have the same period as \(y=\sin x\), which is \(2 \pi\), but the height of the curve will be five times greater.
03

Graph the function y=sin x

Next, plot the function \(y=\sin x\) in the same coordinate system from 0 to \(2 \pi\). This will create a standard sine wave with amplitude of \(1\). Compare this graph with \(y=5 \sin x\) to observe the differences.

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