solving for t (daylight hours problem)?
i'm trying to solve the following problem for t: 720 = 11.895 + 2.545 sin [(2pi/366)(t-80)]. my formula is using the format y = d + a cos [b(t-c)]
I found a similar problem/solution online but don't quite understand how they solved the steps in bold... could someone explain how they got those answers in more detail?:
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
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?
- math - drwls, Saturday, August 13, 2011 at 10:13pm(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.