Question 922475: Please explain how I would go about figuring out the graph to:
-6cos(4x-π/2)
amp = 6
period = 1/2
phase shift = π/8
If I have the above correct from that point what would I do? I am confused because I don't know what to do with the period? I've worked with radians but what does 1/2 period mean? please explain
how this is solved.
Thank you
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Please explain how I would go about figuring out the graph to:
-6cos(4x-π/2)
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Form of equation for cos function:
y=Acos(Bx-C), A=amplitude, period=2π/B, phase shift=C/B
..
For given function:y=-6cos(4x-π/2)
A=6
B=4
Period=2π/4=π/2
1/4 period=π/8
C=π/2
Phase shift=C/B=(π/2)/4=π/8 (shift to the right)
The negative sign means the basic curve is reflected about the x-axis.
..
Graphing the function for one period:
Start with basic cos curve with amplitude 1 and no phase shift.
Mark x-axis at 1/4 period intervals(π/8)in radians.
(0,1),(π/8,0),(2π/8,-1),(3π/8,0),(4π/8,1)
..
multiply y-coordinates by -6(amplitude)
(0,-6),(π/8,0),(2π/8,6),(3π/8,0),(4π/8,-6)
..
shift x-coordinates π/8 to the right.
(π/8,-6),(2π/8,0),(3π/8,6),(4π/8,0),(5π/8,-6)(Final configuration)
..
y-intercept
set x=0
y=-6cos(4x-π/2)
y=-6cos(-π/2)=-6*0=0
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