Question 591178: find the graph of the equation, and the period and phase shift. y=sin(1/4x+pi/3)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find the graph of the equation, and the period and phase shift.
y=sin(1/4x+pi/3)
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Equation used for graphing sin functions: y=Asin(Bx-C), A=amplitude, Period=2π/B, Phase shift=C/B.
For given equation: y=sin(1/4x+pi/3):
A=1
B=1/4
Period: 2π/B=2π/(1/4)=8π
1/4 period=8/4=2π
phase shift: C/B=(π/3)/(1/4)=4π/3 (shift to the left)
..
Graph for one period:
scale of x-axis in radians
With no phase shift, (x,y) coordinates for the given sin function would be as follows:
(0,0), (2π,1), (4π,0), (6π,-1), (8π,0)
..
A phase shift of 4π/3 radians would shift x-coordinates to the left as follows:
(-4π/3,0), (2π/3,1), (8π/3,0), (14π/3,-1), (20π/3,0)
..
y-intercept
set x=0
y=sin(π/3)
y=√3/2
You now have all the points you need including the y-intercept to plot given sin function.
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