Question 402890: Stuck on this problem...please help!!
Calculate the amplitude, period, phase shift, and use the information to sketch one full cycle of the graph of the equation f(t) = 0.2 cos (pi/12 t - 7pi/12), which is used in predicting the height of ocean tidal components.
Thank you!!
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Stuck on this problem...please help!!
Calculate the amplitude, period, phase shift, and use the information to sketch one full cycle of the graph of the equation f(t) = 0.2 cos (pi/12 t - 7pi/12), which is used in predicting the height of ocean tidal components.
Thank you!!
..
The standard form for the Cos function is,
y=ACos(Bx-C) (B>0),with A=amplitude, Period=2pi/B, Phase shift=C/B
For the given equation,
f(t) = 0.2 cos (pi/12 t - 7pi/12)
A=0.2
B=pi/12
C=7pi/12
Amplitude = 0.2
Period = 2pi/B=2pi/(pi/12)=24 radians
Phase Shift = C/B=(7pi/12)/(pi/12)=7 radians
On the x-axis on a scale of radians, without a phase shift,
starting from zero, the basic cos curve will like this for one full cycle:
(0,0.2),(6,0), (12,-0.2),(18,0),(24,0.2)
With a phase shift of 7, all the x-values will shift right by 7 as follows:
(7,0.2),(13,0), (19,-0.2),(25,0),(31,0.2)
The graphs below show the green curve as the original and the red curve as the original shifted 7 radians:
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