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Expert-verified Found in: Page 410 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # Write the equation of a sine function that has the given characteristics.Amplitude: $3$Period: $\mathrm{\pi }$

Equation of a sine function is $y=±3\mathrm{sin}\left(2x\right)$

See the step by step solution

## Step 1. Given information

We have to write the equation of a sine function that has:

$A=3\phantom{\rule{0ex}{0ex}}T=\mathrm{\pi }$

## Step 2. Find the equation of a sine function

To find the equation, refer the form $y=A\mathrm{sin}\left(\omega x\right)$

and role="math" localid="1646330674044" $\omega =\frac{2\mathrm{\pi }}{T}$

Solving for $\omega$,

$\omega =\frac{2\mathrm{\pi }}{T}\phantom{\rule{0ex}{0ex}}\omega =\frac{2\mathrm{\pi }}{\mathrm{\pi }}\phantom{\rule{0ex}{0ex}}\omega =2$

Substitute the values,

We have role="math" localid="1646330752384" $y=±3\mathrm{sin}\left(2x\right)$ ### Want to see more solutions like these? 