Question 703423: Sketch the graph of y=2+3sin(2x+π/4). Include at least 2 full periods. State the period, amplitude, phase shift and vertical shift.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Sketch the graph of y=2+3sin(2x+π/4). Include at least 2 full periods. State the period, amplitude, phase shift and vertical shift.
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Equation for sin function: y=Asin(Bx-C), A=amplitude, period=2π/B, phase shift=C/B
For given equation: y=2+3sin(2x+π/4)
Amplitude=3
B=2
period=2π/B=2π/2=π
1/4 period: π/4
C=π/4
phase shift=C/B=(π/4)/2=π/8 (shift to the left)
vertical shift: 2 units up
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Graphing:
I don't have the means to draw the graph but I will show you how to develop the coordinates with which you can use to draw the graph your self.
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Coordinates for 2 periods with amplitude=1 and no phase shift: (basic sin curve with period=π
(0,0), (π/4,1), (π/2,0), (3π/4,-1), (π,0), (5π/4,1), (3π/2,0), (7π/4,-1), (2π,0)
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Increase amplitude=3:
(0,0), (π/4,3), (π/2,0), (3π/4,-3), (π,0), (5π/4,3), (3π/2,0), (7π/4,-3), (2π,0)
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horizontal shift π/8 to the left:
(-π/8,0), (π/8,3), (3π/8,0), (5π/8,-3), (7π/8,0), (9π/8,3), (11π/8,0), (13π/8,-3), (15π/8,0)
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vertical shift 2 units up: (final configuration)
(-π/8,2), (π/8,5), (3π/8,2), (5π/8,-1), (7π/8,2), (9π/8,5), (11π/8,2), (13π/8,-1), (15π/8,2)
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