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Chapter 5: Problem 13

Determine the amplitude and period of each function. Then graph one period of the function. $$y=-3 \sin 2 \pi x$$

Short Answer

Expert verified
The amplitude of the function \(y=-3 \sin 2 \pi x\) is 3 and its period is 1.

Step by step solution

01

Determine the amplitude

Amplitude is given by the absolute value of the coefficient of the sine function. In this case, the coefficient of the \(\sin\) function is -3, so the amplitude is \(\|-3\|=3\).
02

Determine the period

The period is determined by \(P=2\pi/B\), where B is the coefficient of x in the argument of the sine function. Here, \(B=2\pi\), thus \(P=2\pi/2\pi=1\).
03

Graph the function

Now that we know the amplitude (3) and the period (1), we can draw the graph of the function. Remember that this is a negative sine function, so it will be reflected over the x-axis. The graph starts from the origin (0,0), reaches down to the minimum point (-3), goes back to zero (completing the half period), reaches the maximum point (3) and returns to zero (completing one full period). The graph then repeats this pattern.

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