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- April 29th 2009, 04:57 PM #1

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- Apr 2009
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## sin a = t.a

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.

...Problem background...

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?

- April 29th 2009, 05:04 PM #2

- April 29th 2009, 06:42 PM #3

- Joined
- Apr 2009
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