# What is the answer for question 4. a) http://postimg.org/image/ypiv1yj7r/

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### 1 Answer

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.