Chapter 6: Q 18. (page 409)

Determine the amplitude and period of each function without graphing.
$y = \frac{4}{3} \sin (\frac{2}{3} x)$ .

Short Answer

Expert verified

The amplitude is $\frac{4}{3}$ and period is $3 π$ .

Step by step solution

Step 1. Given Information.

Determine the amplitude and period of each function without graphing.

$y = \frac{4}{3} \sin (\frac{2}{3} x)$ .

Step 2. Evaluation.

For $ω > 0$ , the amplitude and period of $y = A \sin (ω x)$ is given by

Amplitude $= |A|$ , period $= \frac{2 π}{ω}$ .

By comparing the equation , we get

role="math" localid="1647250875837" $A = \frac{4}{3}, ω = \frac{2}{3}$ .

Then, $T = \frac{2 π}{\frac{2}{3}} = 3 π$ .

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Determine the amplitude and period of each function without graphing.
$y = \frac{4}{3} \sin (\frac{2}{3} x)$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Evaluation.

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Step 2. Evaluation.

One App. One Place for Learning.

Most popular questions from this chapter

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Determine the amplitude and period of each function without graphing.
$y = \frac{4}{3} \sin (\frac{2}{3} x)$ .