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

Sep 16, 2017

#### 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 $\frac{\pi}{4}$ to the right.

First look at the graph of sin:

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 $\pi$, $2 \pi$, $3 \pi$.... and $- \pi$, $- 2 \pi$ 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 $\frac{\pi}{4}$ to the right - if you compare this graph and the one above, you can see it's just moved over slightly.:

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:

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