Taylor Series Approximation to Cosine

If a function has a Taylor series that is convergent to the function, it is customary to expect that partial sums with more terms provide a better approximation than those with fewer terms. As the example of y = cos(x) shows, this statement must be qualified.

For x large in absolute value, higher degree polynomials provide worse approximation than lower degree polynomials. For such x, the best approximation is given by the constant term y = 1.

Graphs of Functions

• Cartesian Coordinate System
• Addition and Subtraction of Functions
• Function, Derivative and Integral
• Graph of a Polynomial
• Graph of a Polynomial Defined by Its Roots
• Inflection Points of Fourth Degree Polynomials
• Lagrange Interpolation
• Linear Function
• Taylor Series Approximation to Cosine

Copyright © 1996-2008 Alexander Bogomolny