convert rotation in degrees to percent to move an object x and y directions So I have been out of school for a very long time and have a forehead slapping question: $$ m = \tan(\theta) $$ where $ \theta $ is an angle, but all that gives me is $ \frac yx $. I need to know how far something should move in each vector given that it is pointed at a certain angle. How is this determined?

Let's say a point moved for point $(x_1, y_1)$ to $(x_2, y_2)$ , then we know the point has moved $ x_2 - x_1 $ along x-axis and $ y_2 - y_1 $ along y-axis.

Given than a point moves $ R $ distance along $ \theta $ direction, let, $ \Delta x $ and $ \Delta y $ be the distance moved forward simultaneously on x-axis and y-axis, then we know, $$ \Delta x = R \frac {\Delta x}{ R } \text{ ,but } \frac {\Delta x}{ R } = \cos \theta \text{ so we have } \Delta x = R \cos \theta $$

And similarly $ \Delta y = R \sin \theta $ !enter image description here