set terminal gif animate delay 75
set xrange[-2*pi:2*pi]
set yrange[-2:2]
set grid
set output "TaylorSin.gif"
set label at 4.9,1.5

set label "n = 1" at 4.9,1.7 tc rgb "red"
plot x notitle, sin(x) notitle
unset label   
set label "n = 3"  at 4.9,1.7 tc rgb "red"                                             
plot x-x**3/6 notitle, sin(x) notitle 
unset label  
set label "n = 5"  at 4.9,1.7 tc rgb "red"                                        
plot x-x**3/6+x**5/120 notitle, sin(x) notitle
unset label  
set label "n = 7" at 4.9,1.7 tc rgb "red"                                                  
plot x-x**3/6+x**5/120-x**7/5040 notitle, sin(x) notitle
unset label
set label "n = 9" at 4.9,1.7 tc rgb "red"                                             
plot x-x**3/6+x**5/120-x**7/5040+x**9/362880 notitle, sin(x) notitle
unset label
set label "n = 11" at 4.9,1.7 tc rgb "red"
plot x-x**3/6+x**5/120-x**7/5040+x**9/362880-x**11/39916800 notitle, sin(x) notitle
unset label
set label "n = 13" at 4.9,1.7 tc rgb "red"
plot x-x**3/6+x**5/120-x**7/5040+x**9/362880-x**11/39916800+x**13/6227020800 notitle, sin(x) notitle