How do you graph y=3sin(x-pi/4)+2?

1 Answer
Sep 16, 2017

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Explanation:

This a scaling and translation of the basic y=sin x graph.

It is being scaled by a factor of three, then translated (moved) 2 up and pi/4 to the right.

First look at the graph of sin:
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Points to note are that it goes through the origin (0,0) and goes up to 1, and down to -1. It crosses the x axis at pi, 2pi, 3pi.... and -pi, -2pi etc etc.

I have used the Desmos graphing tool to produce these graphs. I'm afraid I've not been able to change the x axis to show pi rather than numerical values but I hope you'll be able to see that it is crossing approximately every 3.14 (pi).

The first step I've done is to move the graph pi/4 to the right - if you compare this graph and the one above, you can see it's just moved over slightly.:
enter image source here

Next, I've scaled it by a factor of 3, which means that it instead of going between 1 and -1, it will be between 3 and -3. Please note that the graph still crosses the x axis in the same places:
enter image source here

Finally, the graph needs to be moved 2 up and this gives you the final answer:
enter image source here