How Does Daylight Vary by Month Using a Sinusoidal Function?

[Calixto]

Daylight sinusoid any help appreciated :)

A person finds that the number of hours of daylight at his home is approximately given by

h = 12 + 4sin[2π/12(m-9)]
where m represents the number of the month (January = 1, February = 2, etc.)

a) At the person's location, how long is the shortest day of the year?

b) Does the person live in the Northern or Southern Hemisphere?

c) The number 12 occurs twice in the formula, but for two different reasons. Explain the real world meaning of each of the 12's.

 

[Hootenanny]

How does one usually find the minimum of a function?

 

[Tedjn]

Also, how does one find the minimum and maximum of sine in particular?