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

1 Answer
Write your answer here...
Start with a one sentence answer
Then teach the underlying concepts
Don't copy without citing sources


Write a one sentence answer...



Explain in detail...


I want someone to double check my answer

Describe your changes (optional) 200

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.

Was this helpful? Let the contributor know!
Impact of this question
11 views around the world
You can reuse this answer
Creative Commons License