# set terminal pngcairo  transparent enhanced fontscale 1.0 size 500, 350 
# set output 'approximate.1.png'
set style fill   solid 0.40 noborder
set format y "%.1f"
set key inside center top vertical Left reverse enhanced autotitles nobox
set encoding utf8
set samples 500, 500
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
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
GPFUN_approx_1 = "approx_1(x) = x - x**3/6"
GPFUN_approx_2 = "approx_2(x) = x - x**3/6 + x**5/120"
GPFUN_approx_3 = "approx_3(x) = x - x**3/6 + x**5/120 - x**7/5040"
label1 = "x - {x^3}/3!"
label2 = "x - {x^3}/3! + {x^5}/5!"
label3 = "x - {x^3}/3! + {x^5}/5! - {x^7}/7!"
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"