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Chapter 5: Problem 12

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 the period is 1.

Step by step solution

01

Calculate Amplitude

In the given function \(y=3 \sin 2 \pi x\), the coefficient of the sine function is 3. Therefore, the amplitude of the function is 3.
02

Calculate Period

In the given function \(y=3 \sin 2 \pi x\), the coefficient of x inside the sine function is \(2 \pi\). Therefore, the period of the function is \(\frac{2 \pi}{2 \pi}\), which simplifies to 1.
03

Draw the Graph

Now graph the function paying close attention to the amplitude and period. Start at \(x = 0\) and end at \(x = 1\) since the period is 1. The sine function starts at 0, reaches a maximum at the \(\frac{1}{4}\) of the period, comes back to 0 at half the period, reaches a minimum at \(\frac{3}{4}\) of the period, and finally comes back to 0 at the end of the period. The maximum and minimum values will be equal to the amplitude and negative amplitude respectively (here, 3 and -3).

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