Question

I am given a circle with radius R and its centre in the point (0,0) and a point P(x,y), situated on the circle ( x*x+y*y=R*R). I have to move the point P in a clockwise direction, on the circle, with an angle Z, and find the coordinates of the new point. Is there any mathematical formula for doing this? Thanks in advance!

Answer 1

Using polar co-ordinates, you can derive the following.

Initially assume (x, y) in cartesian is (r, t) in polar co-ordinates in the following way

x = r * cos(t)
y = r * sin(t)

Now let (x’, y’) be new points after rotating an angle a (anti-clockwise)

x' = r * cos(t + a)
y' = r * sin(t + a)

Expanding them out, you can get the following

x' = r * cos (t) * cos (a) - r * sin (t) * sin (a) 
y' = r * sin (t) * cos (a) + r * cos (t) * sin (a)

x' = x * cos (a) - y * sin (a)
y' = x * sin (a) + y * cos (a)

Now substitute a = -theta (since you mentioned theta in clock wise direction), you will get the new points.