Question

How would I solve this problem for t?
720 = 11.895+2.545sin [2pi/366(t-80.5)]

Answer 1

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(t-80.5)]
278.2338 = sin [2pi/366(t-80.5)]

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.

Answer 2

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

Answer 3

i think i figured out my mistake. it should be

720 = 713.7+152.7 sin [(2pi/366)(t-80.75)]

this problem is modelling minutes of daylight in a town using the form y = d+a sin[b(t-c)]. let y equal 720 minutes of daylight and let t=the number of days in 2012