What was the original problem you had to solve?
I have been working on a problem I have sort of worked myself into, and don't really know how to solve it.
I end up at
k = sin x / (1- cos x)
and I need to solve for x.
I cant find any identities that will make this easier, and I don't really remember how to break it up any further (as I am an engineer, not a mathematician)
I can plug it into a calculator and solve for a given value, and that works well enough for what I am doing. However, I would like to further solve it, to make using it easier in the future.
Anyway you could aide me would be greatly appreciated.
I would like a formula (or a couple of formulas) that allow me to take a given change in X and Y, treat it as a chord of a circle, and determine the angle of the chord and the radius of the circle.
I probably just worked myself into a corner.
Here is where I got:
x = sin theta
y= 1- cos theta
x/y = sin theta / (1-cos theta)
I can use my graphing calc to find theta for a given ratio x/y
Then I plug x and theta back into the first equation and solve for r.
This works... almost. when I build an arc (in a cad prog) based on my calculated r and theta, it gets close, but doesn't quite match up with the original x and y.
This is a tricky problem, requiring special treatment.
We have: .Solve for
Divide by .
Consider angle in a right triangle with: .The hypotenuse isCode:* ____ * | √1+kČ * | * | 1 * | * θ | * - - - - - - - - * k
And: . .
. . Note that: . .
Substitute  into : .
. . And we have: .
. . Then: .
Substitute : .
. . Therefore: .