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Chapter 6: Q 15. (page 409)

Determine the amplitude and period of each function without graphing.
$y = 6 \sin (πx)$ .

Short Answer

Expert verified

The amplitude is 6 and period is 2.

Step by step solution

01

Step 1. Given Information.

Determine the amplitude and period of each function without graphing.

$y = 6 \sin (πx)$ .

02

Step 2. Evaluation.

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

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

On comapring, we get

$|A| = 6$ , $ω = π$

$T = \frac{2 π}{π} = 2$ .

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