arcsinx=x+ 1/6x^3+o(x^3)。

tanx=x+ 1/3x^3+o(x^3)。

cosx= 1- 1/2x^2+ 1/24x^4。

ln( 1+x)=x- 1/2x^2+ 1/3x^3+o(x^3)。

In mclaughlin's formula,

Error |R? (x)| is the ratio of x when x→0? High-order infinitesimal, if the function f(x) has a derivative of order up to n+ 1 in the open interval (a, b), when the function is in this interval, it can be expanded into the sum of a polynomial about x and a remainder. Mclaughlin formula is a special form of Taylor formula.