# How do you graph y=3sin(1/3x+ pi/2)-2?

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Apr 1, 2018

As below.

#### Explanation:

$y = A \sin \left(B x - C\right) + D$

Given equation is $y = 3 \sin \left(\left(\frac{x}{3}\right) + \left(\frac{\pi}{2}\right)\right) - 2$

$A m p l i t u \mathrm{de} = | A | = 3$

$\text{period } = \frac{2 \pi}{|} B | = \frac{2 \pi}{\frac{1}{3}} = 6 \pi$

$\text{Phase Shift " = C / B = (-pi/2) / (1/3) = -(3pi)/2, " " (3pi)/2 " to the left}$

$\text{Vertical Shift } = D = - 2$

graph{3 sin((x/3)+(pi/2))-2 [-10, 10, -5, 5]}

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