Can you help me build a simple formula?

I'm not in school, and I'm not looking for any answer to any homework assignment. I have something I'm doing on my own, and I wanted to see if anyone comes up with the same formula, or close to it, as I did for the following.

Take a graph: draw a line so that , which we know is a angle and a angle from heading in a positive and negative direction on to infinity.

Now, let's say that the line goes to then then etc. What formula would also extend the line to ...ect., as the line extends positively?

In other words, you start from and the vectors extend positively, and negatively in proportion to each other. When the vector goes from to to it then extends to at the same time to , , etc.

I understand people have their own work and may not want to be sidetracked with this, but I do appreciate anything anyone has to suggest. My guess is this is a well-known formula, and I'm just don't know well enough to know it. Nevertheless, I want to get this simple formula down before proceeding on with my work.

Thank you very much in advance for anything.

Ed