I am hoping this is a very simple equation that can solve this (I am not a mathematician) but considering I have values in degrees (0 - 360), I am trying to convert that back into plus and minus X and Y values. So between 0 and 180 degrees it is a positive X value (180-360 being negative X) and between 90 and 270 degrees it would be a positive Y (270-90 being negative Y). For example if I am facing North West it is a value of 45 degrees and I want to convert that to 0.5+Y and 0.5-X. North is +1Y, 0X and East is +1X, 0Y etc.
Is this straightforward, I will add a diagram if required, thanks
Use the fact that there is a correspondence between the points $(x, y)$ in the Cartesian plane and the points $(r, \theta)$ in polar coordinates given by $x = r \cos \theta$ and $y = r \sin \theta,$ where $r$ is the radius and $\theta$ is the angle. One can see this by observing that one can always draw a circle centered at the origin starting and ending at a point $(x, y)$ in the plane with radius $r = \sqrt{x^2 + y^2}.$ Our angle $\theta$ is the angle from the $x$-axis taken counterclockwise, e.g., $\theta = \pi = 180^\circ$ gives the point diametrically opposite to the point on the circle of radius $r = \sqrt{x^2 + y^2}$ that lies on the $x$-axis, i.e., $(-r, 0).$
Considering that you want due north to coincide with the point $(0, 1)$ in the plane, we may take $r = 1.$ Consequently, the formula for a pair $(x, y)$ in terms of the angle $\theta$ is simply $(\cos \theta, \sin \theta).$