Chapter 6: Q 19. (page 409)

Determine the amplitude and period of each function without graphing.
$y = \frac{5}{3} \sin (- \frac{2 π}{3} x)$ .

Short Answer

Expert verified

The amplitude is $\frac{5}{3}$ and period is $- 3$ .

Step by step solution

Step 1. Given Information.

Determine the amplitude and period of each function without graphing.

$y = \frac{5}{3} \sin (- \frac{2 π}{3} x)$ .

Step 2. Evaluation.

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

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

On comparing, we get

Amplitude $= |\frac{5}{3}| = \frac{5}{3}, ω = - \frac{2 π}{3}$ .

Period $T = \frac{2 π}{- \frac{2 π}{3}} = - 3$ .

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Determine the amplitude and period of each function without graphing.
$y = \frac{5}{3} \sin (- \frac{2 π}{3} x)$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Evaluation.

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Short Answer

Step by step solution

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Step 2. Evaluation.

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Determine the amplitude and period of each function without graphing.
$y = \frac{5}{3} \sin (- \frac{2 π}{3} x)$ .