Are my answers correct?
1. In 2001, Windsor, Ontario received its maximum amount of sunlight, 15.28 hrs, on June 21, and its least amount of sunlight, 9.08 hrs, on December 21. On what day(s) can Windsor expect 13.5 hours of sunlight?
I determined the equation for this is D(h) = 3.1cos[360/365(h – 172)] + 12.2. I know the answer is 238 and 106, but was only able to get 238 as a solution:
3.1cos[360/365(h – 172)] + 12.2 = 13.5
3.1cos[360/365(h – 172)] = 1.3
cos[360/365(h – 172)] = 1.3/3.1
360/365(h – 172) = arccos(1.3/3.1)
360/365(h – 172) = 65.20613754
h – 172 = 365/360(65.20613754)
h – 172 = 66.11177834
h = 238.1117783 = 238
I was able to get 106 as a solution by doing the following:
238 – 172 = 66
172 – 66 = 106
What is the proper way of getting 106 as the second solution?
2. A mass suspended on a spring will exhibit sinusoidal motion when it moves. If the mass on a spring is 85 cm off the ground at its highest position and 41 cm off the ground at its lowest position and takes 3.0 s to go from the top to the bottom and back again, determine an equation to model the data.
I was able to determine the following:
A = 22
B = 120
D = 63
So H(t) = 22sin[120(h – C) + 63
I was unable to determine the C value, but by plugging in this formula into graphing software and playing around the numbers, I got 2.25 as the C value, but not sure how to get this answer from the given data…