Chapter 9.10, Problem 59E

a)

To determine

Find the first four non-zero terms of the Taylor series for the function ${\sin }^{-1}x$ using binomial series $\frac{d}{dx}\left({\sin }^{-1}x\right)={\left(1-x^2\right)}^{\frac{-1}{2}}$ and also find the radius of convergence.

b)

To determine

Find the first four non-zero terms of the Taylor series for the function ${\cos }^{-1}x$ using part (a) result.