Q. 59 - Precalculus Enhanced with Graphing Utilities

Question

Write the equation of a sine function that has the given characteristics.

Amplitude: $3$

Period: $\mathrm{\pi }$

Step-by-Step Solution

Answer

Equation of a sine function is $y=\pm 3\sin \left(2x\right)$

Step 1. Given information

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

$$\begin{gathered} A=3 \\ T=\mathrm{\pi } \end{gathered}$$ 

Step 2. Find the equation of a sine function

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

and $\omega =\frac{2\mathrm{\pi }}{T}$

Solving for $\omega$,

$$\begin{gathered} \omega =\frac{2\mathrm{\pi }}{T} \\ \omega =\frac{2\mathrm{\pi }}{\mathrm{\pi }} \\ \omega =2 \end{gathered}$$

Substitute the values,

We have  $y=\pm 3\sin \left(2x\right)$