Question 959840: a. Let f(x)=3cos(2π(x)+π/2). Find each of the following for f.
i. Amplitude
ii. Period
iii. Phase shift
please describe what each one means and how to derive it from the function
b. Find all solutions 2cos^2 + cos(x) =1
Thank you
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! a. Let f(x)=3cos(2π(x)+π/2). Find each of the following for f.
i. Amplitude
ii. Period
iii. Phase shift
please describe what each one means and how to derive it from the function
equation for cos function: y=Acos(Bx-C), A=amplitude, period=2π/B, phase shift=C/B
For given cos function:f(x)=3cos(2π(x)+π/2)
Amplitude=3
B=2π
period=2π/B=2π/2π=1
phase shift=C/B=(π/2)/2π)=1/4(shift to the left)
..
b. Find all solutions 2cos^2 + cos(x) =1
2cos^2x+cosx-1=0
(2cosx-1)(cosx+1)=0
..
cosx=1/2
x=π/3+2πk, 5π/3+2πk, k=any integer
or
cosx=-1
x=π+2πk, k=any integer
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