So I know, my origin "(0,0)", my angle "theta" degrees, and the distance from the origin, "d"
Now I think I can work this out with polar coordinates, but really have no idea how to go about it. My overall goal is to work out the point that is (x,y) on this diagram.
Given the polar coordinates $(r,\theta)$, to convert it to the Cartesian coordinates is a simple matter of trigonometry.
The $x$-coordinate is how far along the $x$-axis you are, so can be found using the formula $$x=d\cos\theta.$$ This is because, $x$ is the adjacent side and $d$ is the hypotenuse.
The $y$-coordinate is found likewise, so we have: $$y=d\sin\theta$$