Q. 60 - Precalculus Enhanced with Graphing Utilities

Question

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

Amplitude: $2$

Period: $4\mathrm{\pi }$

Step-by-Step Solution

Answer

Equation of a sine function is 

$y=\pm 2\sin \left(\frac{1}{2}x\right)$

Step 1. Given information

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

$$\begin{gathered} A=2 \\ T=4\mathrm{\pi } \end{gathered}$$

Step 2. Find the equation of a sine function

To find the equation, refer the form 

$y=A\sin \left(\omega x\right)$

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

$$\begin{gathered} \omega =\frac{2\mathrm{\pi }}{T} \\ \omega =\frac{2\mathrm{\pi }}{4\mathrm{\pi }} \\ \omega =\frac{1}{2} \end{gathered}$$

Substitute the values,

We have $y=\pm 2\sin \left(\frac{1}{2}x\right)$