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

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Yanel Share
Aug 17, 2017

First begin by sketching the parent sin function, y=sinx. This will help a lot. Make sure to sketch it lightly.

#### Explanation:

Now you can take a look at the function. The first transformation is the 2 before sin. This means your amplitude will be doubled. Sketch the graph of y=2sinx (also lightly).

The next transformation is the 2 before x. While graphing trig functions, if there is a coefficient of x and something is being added to x within the parentheses, then you need to take the coefficient out of the added number as well, in order to get the accurate horizontal shift.

For example: here, we would want to write it as y=2sin(2(x+$\frac{\pi}{4}$))+3.
The 2 before the x modifies the period of the function. Divide $2 \pi$ by 2 to get the period. The period is $\pi$. That means you need to graph the function with a horizontal compression so that one full cycle of the function takes place between a distance equal to $\pi$ on the x-axis. Graph this transformation, also lightly.

The next step is to use the $\frac{\pi}{4}$ in the parentheses. This is the horizontal shift. The function is adding $\frac{\pi}{4}$, not subtracting it, so that means the function is shifted $\frac{\pi}{4}$ to the left. Graph this transformation, also lightly.

The last step is to shift the function vertically up 3 units. This is your final function, so you don't have to sketch lightly.

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