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We are given this graph:
This is a sinusoid. It is a cosine graph that has not been translated horizontally (or a sine wave with a horizontal translation or phase shift.)
The general form for a cosine function is y=acos(b(x-h))+k where:
a: gives the amplitude (if a<0 the graph is reflected over the horizontal axis.)
b: relates the period (`b=(2pi)/p` where p is the period.)
h: gives the horizontal translation or phase shift
k: gives the vertical translation. (The line y=k is the midline.)
Here the maximum=50 and the minimum is 10.
The amplitude is `a=("max"-"min")/2=(50-10)/2=20` . There is no phase shift. The graph has a period of 2 so `b=(2pi)/2=pi` . And finally the midline is found by `("max"+"min")/2=(50+10)/2=30` .
Thus the function is `y=20cos(pit)+30` ; y is height measured in cm and t is time in seconds. The period is 2 seconds and represents the time for the pedals to make 1 full revolution.
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