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

Aug 11, 2018 Note: The two vertical lines are one period of the function placed at $x = \frac{\pi}{3}$ and $x = \frac{7 \pi}{3}$. 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: $2 \pi$ (nothing to change here)
phase shift: $\frac{\pi}{3}$ to the right (change start point to the right $\frac{\pi}{3}$)
vertical shift: up 2 (shift the start point from ($\frac{\pi}{3}$,0 to $\frac{\pi}{3}$,2)

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