What is the series expansion of sin^-1(x) at x = 0. Please give 3-5 terms of the expansion with steps if possible.Thanks for your help.

Guest Jun 12, 2017

#1**+1 **

Taylor Series around x = 0

x + x^3/6 + (3 x^5)/40 + (5 x^7)/112 + (35 x^9)/1152 + (63 x^11)/2816

CPhill
Jun 12, 2017

#2**0 **

Taylor series expansion can be used here as follows:

Series expansion at x = 0:

Sin^-1(x) =x + x^3/3! + 3^2.x^5/5! + 3^2.5^2.x^7/7! + 3^2.5^2.7^2.x^9/9! + 3^2.5^2.7^2.9^2.x^11/11!.......and so on.

This is the same as:

Sin^-1(x) = x + [1/2.3]x^3 + [1.3/2.4.5]x^5 + [1.3.5/2.4.6.7]x^7 + [1.3.5.7/2.4.6.8.9]x^9....etc.

The steps here are self-explanatory.

Guest Jun 12, 2017