Question 691292: Find the amplitude, period, and phase shift of the function, and graph one completed period:
y=1+COS (3X+pie/2)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the amplitude, period, and phase shift of the function, and graph one completed period:
y=1+COS (3X+pie/2)
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Equation for the cos function: y=A)cos(Bx-C), A=amplitude, period=2π/B, phase shift=C/B
For given equation: 1+cos(3x+π/2)
Amplitude=1
B=3
period: 2π/B=2π/3
1/4 period=2π/12=π/6
phase shift=C/B=(π/2)/3=π/6 (to the left)
..
Graphing:
I don't have the means to graph the function for you, but I can show you how to develop the coordinates with which you can draw the graph:
Start with the basic function: y=cos x with a period of 2π/3
coordinates: (0,1), (π/6,0), (π/3,-1), (π/2,0), (2π/3,1)
shift to left (π/6): (-π/6,1), (0,0), (π/6,-1), (π/3,0), (π/2,1)
bump up 1 unit: (-π/6,2), (0,1), (π/6,0), (π/3,1), (π/2,2) (final configuration
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