Question

The maximum angle of the sun above the horizon for a small town in Ontario was recorded on the 21st of each month and is displayed in the table below.
Graph the data and create a sinusoidal equation to model the data

Month Angle
1 25
2 35
3 45
4 56
5 65
6 68
7 65
8 56
9 45
10 35
11 25
12 22

Answer 1

y(11) = y(1) so the period is 10
The amplitude is (68-25)/2 = 21.5
The middle value is (68+25)/2 = 46.5
The maximum value is at x=6
y = 46.5 + 21.5 cos(π/5 (x-6))
or, since the middle value is at x = 3.5,
y = 46.5 + 21.5 sin(π/5 (x-3.5))