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

1 Answer
Daft
Sep 16, 2017

enter image source here

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:
enter image source here

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

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