Would you please clarify as to why the period is 2pi? I can see the difference in the x value of the maximum and minimum is pi, but I don't know how you deduced that the period is twice as much? Thank you.
Since the difference between the maximum and the minimum is pi, the difference between the minimum and the next maximum is also pi. This means that the distance between any two maximums is 2pi. I hope this clears it up.
Also, in my book the formula for the COS function is given as f(x) = a cos b(x - h) + k. In your solution, we have calculated a, h, and k. However, we did not calculate 'b' and did not utilize the period. Can you explain that, as well? Thank you.
The equation should actually be f(x) = a cos (bx -h) + k. The normal period of a cosine graph is always 2pi, so in this case b = 1. You can show this through the equation y = cos(x). The period of this graph is 2pi and the b value is 1.