The best approximation of tan(x) you have ever seen: Padè approximation

I apologize if the English text will sound a little strange, but I used an online translator and I'm not sure if it translated my words correctly. However, help yourself with the formulas, luckily those do not change whatever language is spoken.

[idjles]

I plotted this in Excel. You cannot see the difference between tan(x) and Pade(x) over the range 0 to pi. It is mostly 3-5 decimal places BETTER than than Taylor series, and it handles the asymptote at pi/2 REALLY WELL on BOTH sides of Pi/2. and the ALGEBRAIC zeroes of the denominator give a VERY GOOD approximation to Pi/2. Incredible!!

[guisimoso]

This is fantastic! I plotted this and it is really good, imagine with more terms

[mikeshlyak]

A polynomial divided by another polynomial will always be more powerful than taylor.

[Hjerpower]

you could have set a=1 to work with less variables because you can scale everything