size 11 8

! Based on example by Pascal B.

include "graphutil.gle"

set texlabels 1
begin graph
  scale auto
  title "Sine Function Approximation"
  xtitle "$x$"
  xaxis min 0 max 10
  yaxis min -3 max 3
  ytitle "$f(x)$"
  key pos tr hei 0.25
  let d100 = sin(x)
  let d101 = x
  d100 line color autocolor(1) key "$\sin(x)$"	
  d101 line color autocolor(2) key "order = $1$"
  let d1 = x
  factorial = 1
  for order = 2 to 5
    n = order-1
    factorial = factorial*(2*n)*(2*n+1)
    let d[order] = d[order-1]+(-1)^(n)*(x^(2*n+1))/factorial
    d[order] line color autocolor(order+1) key "order = $"+num$(order)+"$"
  next order   
end graph