Use Taylor expansion of (1+X) A to transform x into-x^2.
Because the derivative of arctan is equal to1/(1+x 2).
So the Taylor expansion of the arctangent derivative is 1-x 2+x 4-x 6+ ... and we get:
arctan(x)= x-(x^3)/3+(x^5)/5-(x^7)/7+) ....
The approximate value of arctan0.8 calculated by the third-order Taylor formula is 0.8-0.8 * 0.8 * 0.8/3, and the error is about (0.8 5)/5.
Taylor formula
It is a formula that uses the information of a function at a certain point to describe the value near it. If the function meets certain conditions, Taylor formula can use the derivative values of each order of the function at a certain point as coefficients to construct a polynomial to approximate the function.
Taylor formula is named after British mathematician Brook Taylor, who first described it in a letter 17 12. Taylor formula is one of the commonly used approximate methods to study the properties of complex functions, and it is also an important application content of function differential calculus.