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!!

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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:


{{{graph(400,300,-0,30,-.4,.4,.2cos((3.14/12)x- (7)(3.14)/12),.2cos((3.14/12)x- 0))}}}