Question

In Philadelphia the number of hours of daylight on day t (where t is the number of days after Jan. 1) is modeled by the function
L(t)= 12+2.83sin(2pi/365(t-365))

A) Which days of the year have about 10 hours of daylight?
B) Which days of the year have more than 10 hours of daylight?

Answer 1

(A) Solve
10 = 12 + 2.83 sin[(2*pi/365*(t-365)]

-2 = 2.83 sin[(2*pi*/365)(t-365)]
-0.7067 = sin[(2*pi*/365)(t-365)]
sin[(2*pi*/365)(t-365)] = -0.7848
Solve for t.

[(2*pi*/365)(t-365)] = -0.90244
Use the first value

t-365 = -52
t = 313 days
Oct 1 is day 303. So Oct 11 is one answer. The other day will be 52 days after the winter solstice, or about Feb 11.