Its been a while since I really had to deal with an equation like this, and I might just be missing a simple trig identity. I would really appreciate any help you might be able to give me.
I don't believe I have made any mistakes getting here because I can extrapolate the solution from a graphing calc, and the solution works in my application.
I am trying to solve for Θ in the following equation (I am working in degrees):
ΔL = (π * r * Θ / 45) - (4 * r * sinΘ)
The Triangle is a "delta". It signifies a change in that value. In this case, I am working out the change in length of a series of arcs that starts and ends at the same points of a straight line.
Yes, working with degrees when using PI can be confusing, and I could change it, but the CAD program that I am working with works best in degrees, not radians. I apologize for confusing the numbers further.
All of that aside, your equation is correct.