Question 534831: please help me graph this equation: y=2sin(x/2-pi/3)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! please help me graph this equation: y=2sin(x/2-pi/3)
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Equation used to graph sin function: y=Asin(Bx-C), A=amplitude, Period =2π/B, C/B=Phase shift
For given sin function:
A=2
B=1/2
Period: 2π/B=2π/(1/2)=4π
1/4 period=π
Phase shift:C/B=(π/3)/(1/2)=2π/3 (shift to right)
..
Graphing: (For one period)
Let us first graph the basic sin function for one period
On the x-axis make tick marks at π, 2π, 3π and 4π representing one period.
This will give you the following points:
(0,0), (π,1), (2π,0), (3π,-1), (4π,0)
multiply the y-coordinates by 2
(0,0), (π,2), (2π,0), (3π,-2), (4π,0)
add 2π/3 to the x-coordinates (shifting the curve 2π/3 to the right)
(2π/3,0), (5π/3,2), (8π/3,0), (11π/3,-2), (6π,0)
y-intercept
set x=0
0=2(sin -π/3)=-√3/2*2=-1.732
y-intercept=-1.732
You now have these points and the y-intercept with which you can graph the given function:
note: When plotting the curve, you need to convert the y-values to numbers with decimals, ie, 2π/3=2.0944, 5π/3=5.2360, etc
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