Question

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

Answer 1

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:

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.:

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: