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Chapter 4: Problem 7

Determine the amplitude and period of each function. Then graph one period of the function. $$y=\sin 2 x$$

Short Answer

Expert verified
The amplitude of the function \(y=\sin 2x\) is 1 and the period is \(\pi\).

Step by step solution

01

Determine the Amplitude

The amplitude of the function \(y=\sin 2x\) is determined by the coefficient A in front of the sine function. In this case, A=1, so the amplitude is \(|1|=1\).
02

Determine the Period

The period of the function \(y=\sin 2x\) is determined by \(\frac{2\pi}{|B|}\), where B is the coefficient in front of x within the sine function. Here, B=2, so the period is \(\frac{2\pi}{|2|}=\pi\).
03

Graph the Function

Now we can graph one period of the function. Draw the x-axis and y-axis. Mark the x-axis from 0 to \(\pi\). For the y-axis, mark from -1 to 1. The graph of \(y=\sin 2x\) starts at (0,0), rises to (蟺/4,1), falls back to (蟺/2,0), falls to 3蟺/4,-1, and ends at (蟺,0). Connect these points smoothly to get the graph of one period of the function.

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Most popular questions from this chapter

Use a graphing utility to graph each function. Use a viewing rectangle that shows the graph for at least two periods. $$y=\frac{1}{2} \tan (\pi x+1)$$

Graph one period of each function. $$y=\left|2 \cos \frac{x}{2}\right|$$

A clock with an hour hand that is 15 inches long is hanging on a wall. At noon, the distance between the tip of the hour hand and the ceiling is 23 inches. At 3 P.M., the distance is 38 inches; at 6 P.M., 53 inches; at 9 P.M., 38 inches; and at midnight the distance is again 23 inches. If \(y\) represents the distance between the tip of the hour hand and the ceiling \(x\) hours after noon, make a graph that displays the information for \(0 \leq x \leq 24\)

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