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The sine function and its 7th-degree Taylor polynomial, f(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!}. Made by english wikipedia user Ktims. Copied here from english wikipedia ( Link)


Generated with the following gnuplot script, manually colour-matched with the previous chart here for consistency.

set terminal svg size 1600 1200 fname "Times New Roman" fsize 48
set output "taylorsine.svg"
set xzeroaxis lt 0 lw 4
set yzeroaxis lt 0 lw 4
unset border
set key box
set samples 200

set bmargin 0
set lmargin 0
set rmargin 0
set tmargin 0

set xtics axis ("-2π" -2*pi, "-π" -pi, "π" pi, "2π" 2*pi)
set mxtics 2

set ytics axis ("" -5, "" -4, "" -3, "" -2, "" -1, "" 1, "" 2, "" 3, "" 4, "" 5)
set mytics 20

set xrange [-3*pi:3*pi]
set yrange [-5:5]

f(x) = x - (x**3/3!) + (x**5/5!) - (x**7/7!)

plot sin(x) lt 10 lw 4, f(x) lt 12 lw 4


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