how can i derive a function for a real world incident?

i wanted to know is the following steps are what i should do to derive a function for a real world incident (to be more specific Digital Signals and moving objects):

1-i should know all the independant variable that may affect my dependant variable that i want to know about.

2-study the relation between each independant variable and the dependant variable from the point of view for it's(the independant variable like time for example) sign (can't be negative) .

don't know what's next to derive a function to describe it's behavior.and when should i use a cos,tan ,cot in a function (for example u raise a term by 2 then take the square root of it to make sure it is not negative or gets the absolute value for this term).

sorry guys my q might seem silly but i'm not native english so i'm not quite familiar with english terms for mathmatics like real number ,rational ,irrational ,imaginary numbers ..etc

thanks again and sorry for the long post