Question

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

Answer 1

Note: The two vertical lines are one period of the function placed at `x=pi/3` and `x=(7pi)/3`. Don't include the vertical lines when you graph it yourself, they are just visual aids.

Explanation:

First you must know the graph of the `sin` function.
graph{sinx [0, 6.282, -5, 5]}

Next find the amplitude, period, phase shift, and vertical shift.

Amplitude: 4 (function is four times higher
period: `2pi` (nothing to change here)
phase shift: `pi/3` to the right (change start point to the right `pi/3`)
vertical shift: up 2 (shift the start point from (`pi/3`,0 to `pi/3`,2)

Summary of translations: This is a sin function that has been shifted over `pi/3` so one period of the function will go from `pi/3`to `(7pi)/3` (side note: `(7pi)/3` = `(2pi+pi/3)`). each point on the graph is multiplied by 4, because that is our amplitude. And it has been shifted up two units.