How would I solve this problem for t?
720 = 11.895+2.545sin [2pi/366(t-80.5)]
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(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.
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)(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
To solve the equation 720 = 11.895 + 2.545sin [2π/366(t-80.5)] for t, you can follow these steps:
Step 1: Rearrange the equation.
Start by subtracting 11.895 from both sides of the equation:
720 - 11.895 = 2.545sin [2π/366(t-80.5)]
Step 2: Simplify.
Calculate the left side of the equation:
708.105 ≈ 2.545sin [2π/366(t-80.5)]
Step 3: Isolate the sine function.
To isolate the sine function, divide both sides of the equation by 2.545:
708.105 ÷ 2.545 ≈ sin [2π/366(t-80.5)]
Step 4: Find the inverse sine.
Take the inverse sine (also known as arcsine or sin^-1) of both sides of the equation to isolate t:
sin^-1(708.105 ÷ 2.545) ≈ 2π/366(t-80.5)
Step 5: Solve for t.
Finally, solve for t by rearranging the equation:
t = [366/2π] * [sin^-1(708.105 ÷ 2.545)] + 80.5
Using a scientific calculator, you can substitute the value of [sin^-1(708.105 ÷ 2.545)] and calculate t. Note that [ ] represents the floor function, which rounds down the value inside.
Please remember to use a calculator with radian mode enabled, as trigonometric functions typically work in radians.