Circles, mathematically

My math knowledge is limited, and I would appreciate some help.

How do I find the (x,y) coordinates of a point on a circle's perimeter based on the direction of a ray coming from the circle's origin?

Basically:

Input: Circle's origin coordinates, circle's radius, degree
Output: Coordinates of point where ray (coming from origin of circle) moving in the direction of [degree] hits the perimeter of the circle.

Preferably the degree input is the system of 0-359 degrees, where a number above or below that range would also work just as well, effectively 'wrapping around,' and making 360 work effectively as 0.

Sorry if my diction is poor, I am really not mathematically skilled at all, theory is more my game...

I'll give you an idea of what I'm looking for:

a (circle origin) + radius + (increment/360) = x

b (circle origin) + radius + (increment/360) = y

When [increment] is increased by one, the (x,y) coordinates move along the perimeter of the circle, and when they are decreased by one they move in the opposite direction. 360 is just a placeholder, I'd probably use a smaller number in practice. + is also just a placeholder for whatever is necessary for the equation.