Write the equation of a sine function that has the following characteristics. Amplitude: 4. Period: 7pi. Phase shift: -1/3

Step 1
Write the equation of a sin function that has the following characteristics.
Amplitude $=4---(1)$
Period $=7\pi ----(2)$
Phase shift $=-\frac{1}{3}---(3)$
Since function is
$y=A\sin (wx-\alpha )$
A is Amplitude
By Formula
Period $=\frac{2\text{⧸}\pi }{w}=7\text{⧸}\pi$ from eq (2)
Step 2
$\Rightarrow w=\frac{2}{7}-(4)$
Phase shift $=-\frac{\alpha }{w}$
from eq (3)
$-\frac{1}{2}=-\frac{\alpha }{w}$
Step 3
from eq (4) put w value
$\frac{1}{3}=\frac{\alpha }{\frac{2}{7}}$
$\Rightarrow 3\alpha =\frac{2}{7}$
$\Rightarrow \alpha =\frac{2}{21}$
The appropriate values of complat the sine function
$y=4\sin \frac{2}{7}x+\frac{2}{21}$