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I know the coordinates of one point on a circle, this point is part of a sector. I know the angle of the sector at the centre of radius, I know the radius and I know the arc length. How do I calculate the coordinates of the other coordinate of the sector ?

Picture

I have quickly mocked up the problem in the image above, please note it is B I am aiming to find.

Angle in rads = 0.262

Radius = 21

Arc length = 5.5

A = (0.5,21)

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  • $\begingroup$ You can use complex numbers to calculate the co-ordinates of the new points . Take the init point as $0.5+21i$ and multiply it with $e^{i\theta}$ where $\theta = $ the radians by which it is rotated $\endgroup$ – abkds Mar 5 '14 at 12:20
  • $\begingroup$ In contrast to your other question, this time you have too much information. The radis and angle tell you the arclength. $\endgroup$ – bubba Mar 5 '14 at 12:23
  • $\begingroup$ The center is at distance $21$ from $(0.5,21),$ so it can't be $(0,0).$ On the other hand, if the distance is just very slightly greater than $21$ then $(0,0)$ can be the center. At least some of the numbers must be approximations since $21\times0.262 = 5.502$ (not $5.5$). $\endgroup$ – David K Dec 22 '18 at 5:44
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Same technique as in your other question here.

Let $A = (x,y)$ and let $B= (x_1, y_1)$. Then $$ x_1 = \; x\cos(0.262) + y\sin(0.262) \\ y_1 = -x\sin(0.262) + y\cos(0.262) \\ $$

This assumes the center is again at $(0,0)$.

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