Trig Function Animations Amy Su Sin and Cos restart; with(plots): with(plottools): all:= circle([0,0], 1, color=gold, thickness=2), # circle axis line([-1.25,0], [1.25,0]), line([0,-1.25], [0,1.25]), # sin axis line([2,0], [9.5,0]), line([2.5,1.25], [2.5,-1.25]), textplot({[7,-2,"y = sin 0"], [7,-2,"-"]}, align=LEFT), # cos axis line([0,-2], [0,-9.5]), line([1.25,-2.5], [-1.25,-2.5]), textplot({[3.5,-5.5,"x = cos 0"], [3.5,-5.5,"-"]}, align=LEFT): plist:=NULL: for t from 0.001 by 6.28/48 to 12.57 do: plt:= line([0,0], [cos(t),sin(t)], color=gold, thickness=2), textplot({[.6*cos(t-Pi/6),.6*sin(t-Pi/6),"0"], [.6*cos(t-Pi/6),.6*sin(t-Pi/6),"-"]}), # sin graph plot([cs/2+2.5, sin(cs), cs=0..t], color=red, thickness=2, numpoints=trunc(10*t)+2), line([cos(t),sin(t)], [t/2+2.5,sin(t)], color=red, thickness=2), textplot({[t/2+2.5,-.4,"0"], [t/2+2.5,-.4,"-"]}), textplot([t/2+2.75,sin(t)/2,"y"], align=RIGHT), line([t/2+2.5,sin(t)], [t/2+2.5,0], color=red, thickness=2), # cos graph plot([cos(cs), -cs/2-2.5, cs=0..t], color=blue, thickness=2, numpoints=trunc(10*t)+2), line([cos(t),sin(t)], [cos(t),-t/2-2.5], color=blue, thickness=2), textplot({[-.4,-t/2-2.5,"0"], [-.4,-t/2-2.5,"-"]}), textplot([cos(t)/2,-t/2-2.55,"x"], align=BELOW), line([cos(t),-t/2-2.5], [0,-t/2-2.5], color=blue, thickness=2): plist:=plist, display([all, plt]): od: display([plist], axes = none, scaling = constrained, insequence = true, view = [-1.25 .. 9.5, -9.5 .. 1.25]); Tan and Cot (best at 6/7 fps) restart; with(plots): with(plottools): all:= circle([0,0], 1, color=gold, thickness=2), # circle axis line([-4,0], [4,0]), line([0,-4], [0,4]), # tan lines line([1,-4], [1,4], color=green), line([-4,1], [4,1], color=yellow), # tan axis line([5,0], [12.5,0]), line([5.5,-4], [5.5,4]), textplot({[10,-.4,"tan 0"], [10,-.4,"-"]}, align=LEFT), # cot axis: line([0,-5], [0,-12.5]), line([-4,-5.5], [4,-5.5]), textplot({[-.4,-9,"cot 0"], [-.4,-9,"-"]}, align=LEFT): th:=evalf(arctan(4)): hide:= plot([5.5+cs/2, tan(cs), cs=Pi/2..evalf(Pi-th)], color=white, thickness=6), plot([5.5+Pi/2+cs/2, tan(cs), cs=Pi/2..evalf(Pi-th)], color=white, thickness=6), plot([5.5+Pi+cs/2, tan(cs), cs=Pi/2..evalf(Pi-th)], color=white, thickness=6), plot([5.5+3*Pi/2+cs/2, tan(cs), cs=Pi/2..evalf(Pi-th)], color=white, thickness=6), plot([cot(cs), -5.5-cs/2, cs=0..evalf(Pi/2-th)], color=white, thickness=6), plot([cot(cs), -5.5-Pi/2-cs/2, cs=0..evalf(Pi/2-th)], color=white, thickness=6), plot([cot(cs), -5.5-Pi-cs/2, cs=0..evalf(Pi/2-th)], color=white, thickness=6), plot([cot(cs), -5.5-3*Pi/2-cs/2, cs=0..evalf(Pi/2-th)], color=white, thickness=6): plist:=NULL: for i from 1 to 97 do t:=0.001+6.28/48*(i-1); plt:= line([0,0], [cos(t),sin(t)], color=gold, thickness=2), textplot({[.6*cos(t-Pi/6),.6*sin(t-Pi/6),"0"], [.6*cos(t-Pi/6),.6*sin(t-Pi/6),"-"]}), # tan graph line([0,0], [1,tan(t)], color=gold, thickness=2), plot([cs/2+5.5, tan(cs), cs=0..t], color=red, thickness=2, numpoints=trunc(10*t)+2, discont=true), textplot({[t/2+5.5,-.4,"0"], [t/2+5.5,-.4,"-"]}), `if`( not (i in {13,14,38,62,86}), plot([[1,tan(t)], [t/2+5.5,tan(t)], [t/2+5.5,0]], color=red, thickness=2), NULL), # cot graph line([0,0], [cot(t),1], color=gold, thickness=2), plot([cot(cs), -cs/2-5.5, cs=0..t], color=blue, thickness=2, numpoints=trunc(10*t)+2, discont=true), textplot({[-.4,-t/2-5.5,"0"], [-.4,-t/2-5.5,"-"]}, align=LEFT), `if`( not (i in {1,2,26,50,74}), plot([[cot(t),1], [cot(t),-t/2-5.5], [0,-t/2-5.5]], color=blue, thickness=2), NULL): plist:=plist, display([all, plt, hide]): od: display([plist], axes = none, scaling = constrained, insequence = true, view = [-4 .. 12.5, -12.5 .. 4]); Csc and Sec (best at 6/7 fps) restart; with(plots): with(plottools): all:= circle([0,0], 1, color=gold, thickness=2), # circle axis line([-4,0], [4,0]), line([0,-4], [0,4]), # csc axis line([5,0], [12.5,0]), line([5.5,-4], [5.5,4]), textplot({[10,-.4,"csc 0"], [10,-.4,"-"]}, align=LEFT), # sec axis line([0,-5], [0,-12.5]), line([-4,-5.5], [4,-5.5]), textplot({[-.4,-8.5,"sec 0"], [-.4,-8.5,"-"]}, align=LEFT): th:=evalf(arcsec(4)): hide:= plot([5.5+cs/2, csc(cs), cs=Pi..evalf(3*Pi/2-th)], color=white, thickness=6, discont=true), plot([5.5+cs/2, csc(cs), cs=evalf(3*Pi/2+th)..2*Pi], color=white, thickness=6, discont=true), plot([5.5+cs/2, csc(cs), cs=3*Pi..evalf(7*Pi/2-th)], color=white, thickness=6, discont=true), plot([5.5+cs/2, csc(cs), cs=evalf(7*Pi/2+th)..4*Pi], color=white, thickness=6, discont=true), plot([sec(cs), -5.5-cs/2, cs=th+.01..Pi/2], color=white, thickness=6, discont=true), plot([sec(cs), -5.5-cs/2, cs=3*Pi/2..evalf(2*Pi-th-.01)], color=white, thickness=6, discont=true), plot([sec(cs), -5.5-cs/2, cs=2*Pi+th+.01..5*Pi/2], color=white, thickness=6, discont=true), plot([sec(cs), -5.5-cs/2, cs=7*Pi/2..evalf(4*Pi-th-.01)], color=white, thickness=6, discont=true): plist:=NULL: for i from 1 to 97 do t:=0.001+6.28/48*(i-1); plt:= line([0,0], [cos(t),sin(t)], color=gold, thickness=2), textplot({[.6*cos(t-Pi/6),.6*sin(t-Pi/6),"0"], [.6*cos(t-Pi/6),.6*sin(t-Pi/6),"-"]}), # csc graph line([cos(t),sin(t)], [0,csc(t)], color=gold, thickness=2), plot([cs/2+5.5, csc(cs), cs=0..t], color=red, thickness=2, numpoints=trunc(10*t)+2, discont=true), textplot({[t/2+5.5,-.4,"0"], [t/2+5.5,-.4,"-"]}), textplot({[t/2+5.5,-.4,"0"], [t/2+5.5,-.4,"-"]}), `if`( not (i in {26,48,74,96}), plot([[0,csc(t)], [t/2+5.5,csc(t)], [t/2+5.5,0]], color=red, thickness=2), NULL), # sec graph line([cos(t),sin(t)], [sec(t),0], color=gold, thickness=2), plot([sec(cs), -cs/2-5.5, cs=0..t], color=blue, thickness=2, numpoints=trunc(10*t)+2, discont=true), textplot({[-.4,-t/2-5.5,"0"], [-.4,-t/2-5.5,"-"]}, align=LEFT), `if`( not (i in {12,38,60,86}), plot([[sec(t),0], [sec(t),-t/2-5.5], [0,-t/2-5.5]], color=blue, thickness=2), NULL): plist:=plist, display([all, plt, hide]): od: display([plist], axes = none, scaling = constrained, insequence = true, view = [-4 .. 12.5, -12.5.. 4]);