I would like to know how to determine at which angle a point lies in an ellipse. Suppose I have an ellipse with semimajor and semiminor of 10 and 5 (see illustration). and suppose the point (8,3) lies in the ellipse , how can i find its angle from the origin? Im not really good at math, can anyone show me a step by step computation?
The ellipse doesn't matter here. The angle is $\arctan \frac 38\approx 0.35877 \approx 20.56^\circ$. The tangent of the angle is defined as opposite(3) divided by adjacent (8) and the arctangent is the inverse function-the angle whose tangent is $\frac 38$.
For more general computer calculations, you can use the Atan2 function, which takes care of worrying about which quadrant the angle is in. Without Atan2, if you asked about $(-8,-3)$ you would again get $\arctan \frac 38$ but then have to remember to add $\pi$ radians or $180^\circ$ but Atan2 does that for you.