Question 446695: graph and label y=3sin(2x-π/3)+1
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! graph and label y=3sin(2x-π/3)+1
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I can't draw a graph for you, but perhaps I can show you how to get the information you will need to draw a graph.
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y=3sin(2x-π/3)+1
Standard form for the sine function: y=Asin(Bx-C), A=amplitude, Period=2π/B and Phase-shift=C/B
For given sin function, A=3, B=2, C=-π/3
Amplitude=3
Period=2π/B=2π/2=π
1/4 period=π/4 or 3π/12
Phase-shift
set 2x-π/3=0, then solve for x
2x-π/3=0
2x=π/3
x=π/6 or 2π/12 (phase-shift to right)
y-intercept
set x=0, then solve for y
3sin(2x-π/3)+1=0
3sin(-π/3)+1
3*-√3/2+1=-1.6
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Drawing the graph
The first point you can mark on the graph is the y-intercept=-1.6
Next, on the x-axis, mark 2π/12, the phase-shift point
continuing on the x-axis, mark a point 1/4 period or 3π/12 further which makes the point=5π/12. Mark 3 more points after this at 8π/12, 11π/12 and 14π/12. Note that these point are 1/4 period apart for one period. You now have the points to plot for one period of the given sine function.
They are:
(0,-1.6),(2π/12,0),(5π/12,4),(8π/12,0),(11π/12,-2),(14π,0)
Hope you can understand enough of it to make it worthwhile.
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