Find a point on a cercle in an orthonormed system given an angle.

63 Views Asked by At

In this inverted orthonormed system, I need to find a formula that gives the x and y coordinates of a point on a circle in function of an angle A that have its top on the center of the circle. I know the radius of the circle (let's say 60) and the position of its center (let say (450;540)).

The angle A is in degrees, if A=0° then y'=540 and x'=450+60. It goes as drawn on the diagram anticlockwise, if A=90° then y'=540-60 and x'=450.

I'm pretty sure it's doable.enter image description here

sorry if the english isn't correct, this is for coding an "AI". Thanks !

1

There are 1 best solutions below

2
On

This is going to be a little funny because your axes are drawn a little differently than I'd expect. To be clear, I'm interpreting that $60$ as the radius (half of a diameter), as in the picture rather than in your text. I'm also assuming $A$ is the interior angle as drawn, in radians rather than degrees.

$$x = 450 + 60 \cos(A)$$ $$y = 540 - 60 \sin(A)$$

Does this seem to give you the results you expect?