If I know a coordinate of a point (red dot on image) of a circle with radius x and i want to rotate it y degrees to the right, how do I get the coordinate of the new point (blue dot on image) ?
thanks
As you are seeking a pair of co-ordinates $\displaystyle \left(x_2,\;y_2\right)$
you could set up a pair of equations in 2 unknowns.
If the circle centre is the origin, then
$\displaystyle \left(x_2\right)^2+\left(y_2 \right)^2=\left(x_1 \right)^2+\left(y_1 \right)^2=r^2$
where the other co-ordinates are known.
Then the area of the triangle between the origin and the 2 points is
$\displaystyle 0.5r^2sin\theta$
and so, your 2nd equation is, using the area of a triangle for which one vertex is the origin
$\displaystyle 0.5r^2sin\theta=0.5|x_1y_2-x_2y_1|$
However, a trigonometric solution will be much simpler.
If you label the acute angle between the negative part of the x-axis, the origin and the red dot "A",
your given angle "B",
and the obtuse angle between the positive part of the x-axis and the blue dot "C",
then use the given co-ordinates to calculate the circle radius and the angle "A",
then calculate "C" and use
$\displaystyle x=rcosC,\;\;y=rsinC$
Let's change some of the notation here. Say that the the coordinates of the red point are $\displaystyle (x,y)$ then the coordinates of the blue point $\displaystyle \left( {x',y'} \right)$ can be found using:
$\displaystyle \begin{array}{*{20}c}{x' = x\cos ( - \phi ) - y\sin ( - \phi )} \\ {y' = x\sin ( - \phi ) + y\cos ( - \phi )} \\ \end{array} $
NOTE. I have changed the notation. $\displaystyle \phi$ is the angle you have called $\displaystyle y$. Also note that you said that you know $\displaystyle \color{red}(x,y)$