The number of hours of daylight on a given day in City A is

The number of hours of daylight on a given day in City A is given by the following? equation, where x is the number of days after January 1.

What is the amplitude of this? function?

What is the period of this? function?

How many hours of daylight are there on the longest day of the? year?

How many hours of daylight are there on the shortest day of the? year?

Solution

Amplitude a = 2

Period = 2pi/(2pi/365) => Period = 365

When sin will be maximum , then hours will be maximum => 2+12 = 14hrs

Minimum hours , when sin is minimum => -2+12=10