trig
posted by anna .
How would I solve this problem for t?
720 = 11.895+2.545sin [2pi/366(t80.5)]

same way you would solve for any equation. collect t stuff on one side, and work your way inside out the expressions till t ia all alone:
708.105 = 2.545sin [2pi/366(t80.5)]
278.2338 = sin [2pi/366(t80.5)]
at this point you are stuck. sin(x) is never more than 1, so there is no way it can be 278.2338
I suspect a typo somewhere. 
It is intuitively obvious that this equation cannot have a solution the way it was written
the sin(anything) has to be a number between 1 and +1
so if 720 = 11.895 + x , the value of x cannot possible fall between  1 and +1
check your typing, or if correctly typed, there is no solution 
i think i figured out my mistake. it should be
720 = 713.7+152.7 sin [(2pi/366)(t80.75)]
this problem is modelling minutes of daylight in a town using the form y = d+a sin[b(tc)]. let y equal 720 minutes of daylight and let t=the number of days in 2012