Let D(t) be the length of the tth day of the year 2013 in Mumbai, India, measured in hours, from sunrise to sunset. Three values are known:
| t days |
47 |
74 |
273 |
| D (t) hours |
11.5 |
12 |
12 |
For locations close to the equator such as Mumbai, the function D(t) is well-approximated by the trigonometry function in the form:
D(t)= a + b cos (2πt/365) + c sin (2πt/365)
1. Find a, b, and c, correct to two decimal places, and thus the model for Mumbai.
2. Use your model to determine the length of longest day of the year in Mumbai (correct to the nearest hundredth of an hour).