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

Write the equation of a sine function that has the following characteristics.
Amplitude: 4, Period: $7\pi$ Phase shift: $-\frac{1}{3}$
Type the appropriate values to complete the sine function.
$y=4\mathrm{sin}\left(?x+?\right)$
(Use integers or fractions for any numbers in the expression. Simplify your answers.)
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Step 1
Write the equation of a sin function that has the following characteristics.
Amplitude $=4---\left(1\right)$
Period $=7\pi ----\left(2\right)$
Phase shift $=-\frac{1}{3}---\left(3\right)$
Since function is
$y=A\mathrm{sin}\left(wx-\alpha \right)$
A is Amplitude
By Formula
Period $=\frac{2\text{⧸}\pi }{w}=7\text{⧸}\pi$ from eq (2)
Step 2
$⇒w=\frac{2}{7}-\left(4\right)$
Phase shift $=-\frac{\alpha }{w}$
from eq (3)
$-\frac{1}{2}=-\frac{\alpha }{w}$
Step 3
from eq (4) put w value
$\frac{1}{3}=\frac{\alpha }{\frac{2}{7}}$
$⇒3\alpha =\frac{2}{7}$
$⇒\alpha =\frac{2}{21}$
The appropriate values of complat the sine function
$y=4\mathrm{sin}\frac{2}{7}x+\frac{2}{21}$