Chapter 10
Polynomial and Series Representations of Functions
10.2 Approximation of Functions: Taylor Polynomials
10.2.3 Taylor Polynomials for `sin x`
We turn now to the sine function, for which calculation of the Taylor polynomials is only slightly more difficult than for the exponential function. The corresponding calculations for the cosine function are very similar and will be left to the exercises at the end of this section.
Activity 2
Calculate the first six Taylor polynomials for `f text[(] x text[)] = sin x`. How many different functions are there among these six polynomials?
Use your graphing tool to graph `f text[(] x text[)]` and these Taylor approximations in a single plotting window.
Use your graphing tool to graph the error functions `sin x - P_n text[(] x text[)]` in a plotting window that is scaled so you can see the distinct error curves.
