The "normal" cartesian coordinates and trig operations use:
x = cos(theta)
y = sin(theta)
and make zero degrees go along the positive X axis, and points sweep anticlockwise as theta increases.
To start at the "6 o'clock" position and rotate clockwise instead, you need:
x = -sin(theta)
y = -cos(theta)
i.e. x and y swapped, and negated.
Hence, to get theta from x and y, use:
theta = atan2(-x, -y); // usually y, x