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

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#### Explanation

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#### Explanation:

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Mar 9, 2018

Amplitude $= 2$

Period $= \pi$

Phase shift $= - \left(\frac{\pi}{4}\right)$ $\textcolor{w h i t e}{a a a} \left(\frac{\pi}{4}\right)$ to the left.

Vertical shift $= 3$

#### Explanation:

Standard form of equation is $y = a \sin \left(b x + c\right) + d$

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

Amplitude $= a = 2$

Period $= \frac{2 \pi}{|} b | = \frac{2 \pi}{2} = \pi$

Phase shift $= - \frac{c}{b} = - \frac{\frac{\pi}{2}}{2} = - \left(\frac{\pi}{4}\right)$ $\textcolor{w h i t e}{a a a} \left(\frac{\pi}{4}\right)$ to the left.

Vertical shift $= d = 3$

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

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