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Chapter 4: Problem 72

Use a graphing utility to graph the function. (Include two full periods.) Be sure to choose an appropriate viewing window. $$y=\frac{1}{100} \sin 120 \pi t$$

Short Answer

Expert verified
The graph of the function \(y=\frac{1}{100}\sin(120\pi t)\) within the window 0 \leq t \leq 0.017 and -0.01 \leq y \leq 0.01 shows a sine wave completing two full cycles.

Step by step solution

01

Identify the key features of the given function

In the function \(y=\frac{1}{100}\sin (120\pi t)\), \(\frac{1}{100}\) is the amplitude of the sine wave, which indicates the maximum absolute value of y, and the term \(120\pi t\) inside the sine function indicates that the function will complete 120 periods in the time range \(0 \leq t \leq 1\). There are no other phase or vertical shifts presented.
02

Find an appropriate viewing window

To include two full periods of the function, the viewing window should cover from t = 0 to t = \(\frac{2}{120} = 0.017\) for the x-axis since one period is \(\frac{1}{120}\), and from y = -0.01 to y = 0.01 for the y-axis due to the amplitude.
03

Graph the function

Use your graphing utility to plot the function using the defined window. The resulting graph should show a sine curve, starting at the origin, that completes two full cycles, rising from y = 0 to y = 0.01, falling to y = -0.01, and returning to y = 0 twice.

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