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...

>>15
Read up on it, it's not a startling fact.

What you appear to want is some sort of linear approximation to the sin function.
We've offered you polynomial approximations of small degree, but any smaller degree and you lose any sense of accuracy in the approximation.

Even with a very simple understanding of the sin function you can see such a approximation is impossible, merely by the nature of the function.

It's not that we haven't thought about it long enough, it's that it doesn't exist.

It's liking asking for a polynomial with integer co-efficients that e or pi satisfy.
Surely you might say considering how long we've been studying these numbers we should have such a simple thing, but we can prove they don't exist.

Similarly I could prove to you that no linear approximation exists, but I doubt you follow even the elementary maths involved in that.

GTFO my /sci/