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I have a problem as follows -

I have an arc, with a point on each end. And angle $a$ is how far the arc goes. I need to find the top right point ($P(w, x)$) in relation to the $r$, $P(x, y)$, and $a$ (Note that the x's in either points are not related; I just made a mistake in the diagram). I drew a diagram to better explain. What would describe it? (This is the diagram).

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It would be nicest if the centre of the circle was at the origin.

But you have not said it is. So let us suppose that the centre is at $(a,b)$. Drag the centre to the origin. That moves $(x,y)$ to $(x-a, y-b)=(x',y')$.

Now rotate $(x',y')$ about the origin, counterclockwise, through the angle $a$, which I will call $\theta$ because I am more comfortable with that name.

We end up at a point $(s',t')$ for which there will be a formula soon.

Now undo our earlier dragging, getting $(s'+a,t' +b)$. That is our answer.

Finally, we show how to obtain $(s',t')$ from $(x',y')$. The relevant rotation formula is $s'=x'\cos\theta-y'\sin\theta,\qquad t'=x'\sin\theta+y'\cos\theta.$

I hope the many symbols do not cause trouble.

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    I mean the centre of the circle, so the coordinates of the "vertex" where the angle $\theta$ is. I could give an answer purely in terms of $a$, $b$, $x$, and $y$. For example, the first coordinate of the endpoint of the angle is $a+(x-a)\cos\theta -(y-b)\sin\theta$, similar expression for second coordinate. Just thought I would give some indication of where it all comes from.2012-12-09