Please see attached image.

Knowing only theta and x, find theta_2 and theta_3

(the green curve is an ellipse inscribed within the reddish unit circle)

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- November 28th 2009, 12:19 PMrainerellipse, unit circle, angles
Please see attached image.

Knowing only theta and x, find theta_2 and theta_3

(the green curve is an ellipse inscribed within the reddish unit circle) - November 30th 2009, 12:50 AMOpalg
__Spoiler__: - November 30th 2009, 01:30 AMsimplependulum
In general , we have

Once the value of is comfirmed ,

we can find out the angle . ( if we keep drawing the lines similarly , a sequence is formed ! ) - December 1st 2009, 09:21 AMrainer
These are very unexpected, interesting responses (to me), which is precisely what I hoped to get by posting this problem.

Opalg, I'm hesitant to say you're wrong, but your answer doesn't work when I graph it. Either it's wrong or I'm making some mistake when I graph it.

Simplependulum, I'm still trying to wrap my head around your response. I had never thought of expressing things in that way.

Here is my solution (obviously not the only one):

First, use the given info-- --to find the semi-minor axis of the ellipse, :

so,

Then, the equations for and are, respectively:

and

You derive these equations by fooling around with (x, y) intercepts and pythagorus' theorem. I won't go into the details unless you really want.

Happily, these equations turn out to be reducible to:

and