Just want to say a big thank you to Georgios, Kitonum, Markiyan & John May for your great help.

I'm teaching a group of Danish tradesmith students A-level maths, and right now we're getting stuck into the wonderful world of vector functions. The exercise I had given them was the situation where 2 people were racing around a circular track at different angular velocities and starting points. The assignment was to first construct a vector function for each person, and then see at what time(s) the slower car is overtaken by the faster car - and from this find the positions where this happens.

They're having a hard time getting their heads around a lot of the material, so I needed a general method that didn't require them having to understand how to find general solutions to trigonometric equations but rather a "plug the numbers in here and see what happens" approach that they can play around with and use in other situations where the vector functions can be more complex and not necessarily harmonic.

Anyway - here's the Maple file I arrived at with your help. Thanks once again.

Regards,  Matthew

henrik-katja_race.mw