Question 593699: State the amplitude, period, phase shift, and vertical shift for Y=2 cos 1/2( theta + pi/2 ) -2 Then graph the function.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! State the amplitude, period, phase shift, and vertical shift for Y=2 cos 1/2( theta + pi/2 ) -2 Then graph the function.
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Use x for theta
Equation for graphing cos functions: y=Acos(Bx-C), A=amplitude,Period=2π/B, Phase shift=C/B
For given equation:
2cos(1/2)(x+π/2)-2:
re-write equation:
2cos(x/2+π/4)-2
Amplitude=2
B=1/2
period=2π/B=2π/(1/2)=4π
1/4 period=π
C=π/4
phase shift=C/B=(π/4)/(1/2)=π/2 (to the left)
curve is bumped down 2 units.
..
Drawing a graph for one period with x-axis scale in radians:
With no phase-shift, coordinates of given cos function are as follows:
(0,2), (π,0), (2π,-2), (3π,0), (4π,2)
..
With phase-shift to the left, x-coordinates are changed as follows:
(-π/2,2), (π/2,0), (3π/2,-2), (5π/2,0), (7π/2,2)
..
With bumping of 2 units down, y-coordinates are changed as follows:
(-π/2,0), (π/2,-2), (3π/2,-4), (5π/2,-2), (7π/2,0)
These are coordinates of the final curve you can graph.
One more item to calculate:
y-intercept
x=0
2cos(x/2+π/4)-2
2cos(π/4)-2
2*√2/2-2=√2-2≈-.59
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