What was the original problem you had to solve?

Results 1 to 6 of 6

- September 30th 2009, 09:10 AM #1

- Joined
- Sep 2009
- Posts
- 7

## Sin x / (1-cos x)

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.

- September 30th 2009, 09:27 AM #2

- September 30th 2009, 10:00 AM #3

- Joined
- Sep 2009
- Posts
- 7

## Original Problem

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:

I know

x = sin theta

y= 1- cos theta

so,

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.

- September 30th 2009, 10:39 AM #4

- Joined
- May 2009
- From
- New Delhi
- Posts
- 153

- September 30th 2009, 11:03 AM #5

- Joined
- Sep 2009
- Posts
- 7

- September 30th 2009, 11:07 AM #6

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 12,026
- Thanks
- 845

Hello, gwammy!

This is a tricky problem, requiring special treatment.

Solve for

Divide by .[1]

Consider angle in a right triangle with: .Code:* ____ * | √1+kČ * | * | 1 * | * θ | * - - - - - - - - * k

And: . .[2]

. . Note that: . .[3]

Substitute [2] into [1]: .

. . And we have: .

. . Then: .

Substitute [3]: .

. . Therefore: .