Question 931952: What is the amplitude, period and phase shift of the following function:
y=1+COS (3x + pi/2)
How would I graph one complete period?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! What is the amplitude, period and phase shift of the following function:
y=1+COS (3x + pi/2)
How would I graph one complete period?
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Equation for cos function: y=Acos(Bx-C), A=amplitude, period=2π/B, Phase shift=C/B.
For given cos function:
A=1
B=3
Period=2π/B=2π/3
1/4 period=(2π/3)/4=2π/12=π/6
C=π/2
Phase shift:C/B=(π/2)/3=π/6 (to the left)
..
Determine coordinates:
set up inequality of cos function for one period
0 ≤ (3x+π/2) ≤ 2π/3
subtract π/2 from each term
-π/2 ≤ 3x ≤ π/6=
divide each term by 3
-π/6 ≤ x ≤ π/2
..
coordinates of graph:
(-π/6,2),(0,1),(π/6,0),(2π/6,1),(3π/6,2)
or
(-π/6,2),(0,1),(π/6,0),(π/3,1),(π/2,2)
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