I'm trying to solve the equation..
sin a = t a ...or rewritten as... sin a - t a = 0
solve to find 'a' for a given value of t
where a is in radians, 0 < a < pi/2
where t < 1, typically 0.7-0.9.
Taking a slice of pizza, measure around the arc of the crust, and then measure the straight chord line across the crust. Given these 2 measurements, it is possible to find the slice angle of the pizza, the angle, etc.
c = arc length
l = chord length
So taking a as the unknown angle of the slice, and let t = l/c, which is a known constant, the solution reduces down to
sin (ang/2) = t . (ang/2)
or by making a = ang/2, the equation can be simplified to
sin a = t.a ...or rewritten as... sin a - t.a = 0
(a is measured in radians)
where (2/pi < t < 1) and (0 < a < pi/2)
However, I can only solve this by trial and error, using iterative techniques, such as Newton iteration. It would be nice if there was a precise solution for the above equation to solve for a.
Anyone got a solution, or is this equation not possible to solve?