Question 606188: Sketch the graph of the functions defined by the equation
y = -2cos[(pi/2) - 2x]
It's not so much the drawing of the graph that troubles me, but the steps on how to arrive at the functions. I have no idea how to do that :(
Someone please explain this to me so I can finally follow the lesson. Thank you!
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Sketch the graph of the functions defined by the equation
y = -2cos[(pi/2) - 2x]
**
Equation for cos function: y=Acos(Bx-C), A=amplitude, Period=2π/B, Phase shift=C/B
Rewrite given equation:
-2cos(-2x+π/2)
Amplitude=2
B=2
Period=2π/B=π
1/4 Period=π/4
C=π/2
Phase shift=C/B=(π/2)/2=π/4 (to the right)
..
Steps for graphing given cos function for one period.
Start with basic cos function, cos(-2x) with amplitude=1 and no phase shift.
Coordinates as follows:
(0,1), (π/4,0), (π/2,-1), (3π/4,0), (π,1)
..
Shifting π/4 to the right
(π/4,1), (π/2,0), (3π/4,-1), (π,0), (5π/4,1)
..
Increase amplitude to 2 and reflect curve around x-axis
(π/4,-2), (π/2,0), (3π/4,2), (π,0), (5π/4,-2)
..
y-intercept:
set x=0
-2cos(-2x+π/2)=-2cos(π/2)=0
y-intercept=0
..
You now have the y-intercept and coordinates to graph given cos function.
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