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Chapter 4: Problem 103

Use a graphing utility to graph two periods of the function. $$y=0.2 \sin \left(\frac{\pi}{10} x+\pi\right)$$

Short Answer

Expert verified
The graph of \(y = 0.2\sin\left(\frac{\pi}{10}x + \pi\right)\) is a sine wave with an amplitude of 0.2, shifted \(\pi\) units to the left, with a period of 20 units. Two periods of the function span from 0 to 40 on the x-axis.

Step by step solution

01

Identifying the Important Components of the Function

The given function is \(y = 0.2 \sin \left(\frac{\pi}{10} x + \pi\right)\). The amplitude is 0.2. The phase shift, indicated by the addition of \(\pi\) inside the sine function, is \(\pi\) to the left. The period of the function is \(\frac{2\pi}{\frac{\pi}{10}} = 20\).
02

Plotting the Curve Using a Graphing Utility

Using a graphing tool, set the plotting area to cover at least \(2*20 = 40\) units, because we want to cover two periods of the function. Plot the function \(y = 0.2\sin\left(\frac{\pi}{10}x + \pi\right)\) on the x-y graph panel. The graph will be a wave with an amplitude of 0.2, a horizontal displacement of \(\pi\) to the left, and a period of 20 units.

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Most popular questions from this chapter

Use a graphing utility to graph each pair of functions in the same viewing rectangle. Use a viewing rectangle that shows the graphs for at least two periods. $$y=0.8 \sin \frac{x}{2} \text { and } y=0.8 \csc \frac{x}{2}$$

Use a vertical shift to graph one period of the function. $$y=\sin x-2$$

Use the keys on your calculator or graphing utility for converting an angle in degrees, minutes, and seconds \(\left(D^{\circ} M^{\prime} S^{\prime \prime}\right)\) into decimal form, and vice versa. Convert each angle to \(D^{\circ} M^{\prime} S^{\prime \prime}\) form. Round your answer to the nearest second. $$50.42^{\circ}$$

Use the keys on your calculator or graphing utility for converting an angle in degrees, minutes, and seconds \(\left(D^{\circ} M^{\prime} S^{\prime \prime}\right)\) into decimal form, and vice versa. Convert each angle to a decimal in degrees. Round your answer to two decimal places. $$30^{\circ} 15^{\prime} 10^{\prime \prime}$$

Use a graphing utility to graph each function. Use a viewing rectangle that shows the graph for at least two periods. $$y=\tan 4 x$$
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