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.


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+#pi/4#))+3.
The 2 before the x modifies the period of the function. Divide #2pi # 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 #pi/4# in the parentheses. This is the horizontal shift. The function is adding #pi/4#, not subtracting it, so that means the function is shifted #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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