Question 541717: I.Find the amplitude, period, and phase shift of the function
II. Sketch the graph
A. 
B. 
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! I.Find the amplitude, period, and phase shift of the function
II. Sketch the graph
A. y =-2cos(1/4)x
Equation for graphing cos function: y=Acos(Bx-C), A=amplitude, Period=2π/B, Phase Shift=C/B.
For given function:
y=-2cos((1/4)x-0)
amplitude=2
B=1/4
Period=2π/B=2π/(1/4)=8π
1/4 period=2π
Phase shift: none
..
Graph function for one period:
On an xy coordinate system with the x-axis scaled in radians:
For basic cos function, plot coordinates as follows:
(0,1), (2π,0), (4π,-1), (6π,0), (8π,1)
multiply y-coordinates by -2 for final configuration of graph
(0,-2), (2π,0), (4π,2), (6π,0), (8π,-2)
..
B. y=-(1/2)sin(2x-(π/3))
Equation for graphing sin function: y=Asin(Bx-C), A=amplitude, Period=2π/B, Phase Shift=C/B.
for given sin function
amplitude=1/2
B=2
Period=2π/2=π
1/4 period=π/4
C=π/3
Phase shift: C/B=(π/3)/2=π/6 (shift to right)
..
On an xy coordinate system with the x-axis scaled in radians:
For basic sin function, plot coordinates as follows:
(0,0), (π/4,1), (π/2,0), (3π/4,-1), (π,0)
multiply y-coordinates by -1/2
(0,0), (π/4,-1/2), (π/2,0), (3π/4,1/2), (π,0)
shift x-coordinates π/6 units to the right (add π/6 to x coordinates)
(π/6,0), (5π/12,-1/2), (2π/3,0), (11π/12,1/2), (7π/6,0)
..
y-intercept
y=-(1/2)sin(2x-(π/3))
x=0
y=-(1/2)sin(-π/3)=-(1/2)*sin(-π/3)=-(1/2)*(-√3/2)=.433
..
Final configuration: (extend curve back to y-intercept)
(0,4.33), (π/6,0), (5π/12,-1/2), (2π/3,0), (11π/12,1/2), (7π/6,0)
..
You now have the coordinates you need to plot the graphs of given functions>
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