#!/usr/local/bin/gnuplot -persist
# set terminal pngcairo  transparent enhanced fontscale 1.0 size 600, 400 
# set output 'approximate.1.png'
set style fill   solid 0.40 noborder
set format y "%.1f" 
set key fixed center top vertical Left reverse enhanced autotitle nobox
unset parametric
set samples 500, 500
set style data lines
set xtics  norangelimit 
set xtics   ("-π" -3.14159, "-π/2" -1.57080, 0.00000, "π/2" 1.57080, "π" 3.14159)
set title "Polynomial approximation of sin(x)" 
set xrange [ -3.20000 : 3.20000 ] noreverse nowriteback
set x2range [ * : * ] noreverse writeback
set yrange [ * : * ] noreverse writeback
set y2range [ * : * ] noreverse writeback
set zrange [ * : * ] noreverse writeback
set cbrange [ * : * ] noreverse writeback
set rrange [ * : * ] noreverse writeback
set colorbox vertical origin screen 0.9, 0.2 size screen 0.05, 0.6 front  noinvert bdefault
approx_1(x) = x - x**3/6
approx_2(x) = x - x**3/6 + x**5/120
approx_3(x) = x - x**3/6 + x**5/120 - x**7/5040
NO_ANIMATION = 1
label1 = "x - {x^3}/3!"
label2 = "x - {x^3}/3! + {x^5}/5!"
label3 = "x - {x^3}/3! + {x^5}/5! - {x^7}/7!"
save_encoding = "utf8"
## Last datafile plotted: "+"
plot '+' using 1:(sin($1)):(approx_1($1)) with filledcurve title label1 lt 3,      '+' using 1:(sin($1)):(approx_2($1)) with filledcurve title label2 lt 2,      '+' using 1:(sin($1)):(approx_3($1)) with filledcurve title label3 lt 1,      sin(x) with lines lw 1 lc rgb "black"