how to write python program to find the value of sinx using while loop and function

Answer 1

Sin(x) is #24 here. The second term contains 3! and the next is 5! (etc) which you can more clearly see at the second link:
http://mathworld.wolfram.com/SeriesExpansion.html

http://math2.org/math/algebra/functions/sincos/expansions.htm

You might want to review this to see the similarity in calculation, and potentially to watch for the pitfall under 'unusual behavior':
https://en.m.wikipedia.org/wiki/Leibniz_formula_for_π

Answer 2

You could do it with a Taylor series (you could just use math.sin but whatever)