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

1 Answer
Aug 11, 2018

Answer:

enter image source here

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.