Question 618238: what is the amplitude, period, verticle shift and phase shift of the graph y= 4cos (2x-3.14/2)? what are the incraments of the graph itself?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! what is the amplitude, period, verticle shift and phase shift of the graph y= 4cos (2x-3.14/2)? what are the incraments of the graph itself?
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Equation of cos function: Acos(Bx-C), A=amplitude, period+2π/B, phase shift=C/B
For given equation: y=4cos(2x-π/2).
Amplitude=4
B=2
period=2π/B=2π/2=π
1/4 period=π/4
C=π/2
phase shift=C/B=(π/2)/2=π/4 (to the right)
Vertical shift: none
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To graph for one period, start with coordinates of basic cos curve with amplitude=1, no phase shift, with 1/4 period increments as follows:
(0,1), (π/4,0), (π/2,-1), (3π/4,0), (π,1)
..
Change amplitude from 1 to 4 as follows:
(0,4), (π/4,0), (π/2,-4), (3π/4,0), (π,4)
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Shift curve π/4 to the right as follows: (final configuration)
(π/4,4), (π/2,0), (3π/4,-4), (π,0), (5π/4,4)
..
y-intercept
set x=0
y=cos(-π/2)=0
To complete the graph, extend the curve back to the y-intercept=0
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To draw the graph of given cos function, start with the y-intercept then plot the coordinates of the final configuration . x-axis scale in radians.
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