Output an Animated Trigonometry Circle

Question

I want you to write a program that outputs a trigonometry circle like the one below. I also want you to animate this circle, having the sine line move along the circumference with the other lines move around it. The minimum number of unique frames is 5. Any lower and your entry will not be counted.

The lines you will need are:

• Sine (Both)
• Cosine (Both)
• Secant
• Cosecant
• Tangent
• Cotangent
• OA (on diagram)

Edit: No longer a limit

This is a code golf challenge, but I want you to get your code to below my code which is written in BBC BASIC.

Note: I will remove this requirement if the challenge is too hard.

My code: BBC BASIC - 185 bytes, 232 characters (Thanks Steve)

a=0:REPEAT:CLS:a+=0.005:CIRCLE600,500,300:s=300*SIN(a)+500:c=300*COS(a)+600:sc=300*1/COS(a)+600:cs=300*1/SIN(a)+500:MOVE600,500:DRAWc,s:DRAWc,500:DRAW600,500:DRAWsc,500:DRAWc,s:MOVE600,500:DRAW600,cs:DRAWc,s:DRAW600,s:WAIT 1:UNTIL0

Answer 1

Mathematica, 142 bytes

Graphics[{Circle[],Line/@{{{c=Cos@t,0},{c,s=Sin@t},{0,s}},{{0,0},{1/c,0},{0,1/s},{0,0},{c,s}}},},PlotRange->{r={-2,2},r}]~Animate~{t,0.01,2Pi}

I'm plotting for angles between 0.01 and 2π which conveniently skips any angles where one of the lines would become actually infinite. You can make a GIF from it by replacing Animate with Table, adding a step width of 0.1 say and then using Export on the result:

So I got a bit bored and thought I'd give the full-blown thing a go (with all lines and colours). I omitted the labels, because they are really annoying to position and just clutter everything up.

Animate[
  c = Cos@t;
  s = Sin@t;
  h = Sign@c;
  v = Sign@s;
  i = .1 h;
  j = .1 v;
  Graphics[{
    Thick,
    Circle[],
    Line /@ {{{c, -s}, {0, 0}, {c, s}}, {{-i, 0}, {-i, j}, {0, 
        j}}, {{-i + c, 0}, {-i + c, j}, {c, j}}, {{c - .1 s, 
        s + .1 c}, {1.1 c - .1 s, 1.1 s + .1 c}, 1.1 {c, s}}},
    Circle[{0, 0}, 0.1, {t, Round[t, Pi]}],
    Blue,
    Line /@ {{{0, 0}, {c, 0}}, {{0, s}, {c, s}}},
    Red,
    Line /@ {{{0, 0}, {0, s}}, {{c, 0}, {c, s}}},
    Darker@Green,
    Line[{{c, 0}, {h, 0}}],
    Cyan,
    Line[{{0, s}, {0, v}}],
    Lighter@Lighter@Magenta,
    Line[{{h, 0}, {1/c, 0}}],
    Darker@Darker@Green,
    Line[{{0, v}, {0, 1/s}}],
    Orange,
    Line[{{0, 1/s}, {c, s}}],
    Lighter@Brown,
    Line[{{1/c, 0}, {c, s}}],
    Gray,
    Line[{{c, 0}, {c, -s}}],
    Lighter@Gray,
    Line[{{c, s}, {h, 0}}],
    Lighter@Pink,
    Line /@ {{{-.45 h, 0}, {-.55 h, 0}}, {{-.45 h, 1/s}, {-.55 h, 
        1/s}}},
    Arrowheads[{-.05, .05}],
    Arrow[{{-.5 h, 0}, {-.5 h, 1/s}}],
    Darker@Cyan,
    Line /@ {{{0, -.45 v}, {0, -.55 v}}, {{1/c, -.45 v}, {1/
         c, -.55 v}}},
    Arrow[{{0, -.5 v}, {1/c, -.5 v}}],
    Dashed,
    Black,
    Line[{{c, s}, 1.3 {c, s}}],
    Lighter@Pink,
    Line /@ {{{0, 0}, {-.5 h, 0}}, {{0, 1/s}, {-.5 h, 1/s}}},
    Darker@Cyan,
    Line /@ {{{0, 0}, {0, -.5 v}}, {{1/c, 0}, {1/c, -.5 v}}}
    }, PlotRange -> {r = {-2, 2}, r}],
  {t, 0.01, 2 Pi}
  ];

Enjoy!

And because this is still a code-golf question I golfed this down as well, to see how short I could get it. Currently, 719 bytes:

Graphics[{Thick,Arrowheads@{-.05,.05},(z=Circle)[],(n=Line)/@{{p={c=Cos@t,s=Sin@t},o={0,0},{c,-s}},{-{i=.1(h=Sign@c),0},{-i,j=.1(v=Sign@s)},{0,j}},{{-i+c,0},{-i+c,j},{c,j}},{p+(q={-.1s,.1c}),1.1p+q,1.1p}},z[o,0.1,{t,Round[t,Pi]}],{e=Dashed,n[{p,1.3p}]},Blue,n/@{{o,a={c,0}},{b={0,s},p}},Red,n/@{{o,b},{a,p}},g=(d=Darker)@Green,n@{a,{h,0}},y=Cyan,n@{b,{0,v}},(l=Lighter)@l@Magenta,n@{{h,0},f={1/c,0}},d@g,n@{{0,v},u={0,1/s}},Orange,n@{u,p},l@Brown,n@{f,p},r=Gray,n@{a,{c,-s}},l@r,n@{p,{h,0}},l@Pink,n/@{q={{-.45h,0},{-.55h,0}},{u,u}+q},Arrow@{q={-.5h,0},u+q},{e,n/@{{o,q},{u,u+q}}},d@y,n/@{q={{0,-.45v},{0,-.55v}},{f,f}+q},Arrow@{q={0,-.5v},f+q},{e,n/@{{o,q},{f,f+q}}}},PlotRange->{r={-2,2},r}]~Animate~{t,0.01,2Pi,0.05}

Answer 2

APL (dzaima/APL), 125 bytes

P5.size←2⌿300
t←0
g←P5.G
z←0 0
P5.draw←{g.bg¯1
g.circle 3⌿90
g.ln a←90×1+z,2 1○t
g.rect a
g.ln 90×1+z,(÷2○t),z,z,⍨÷1○t
t+←.1}

Try it online!

Displays it at the top left corner:

Explanation

P5.size←2⌿300 make a 300x300 canvas

t←0 set angle \$\theta=0.\$

g←P5.G shorten drawing namespace

z←0 0 save [0,0] in z

P5.draw←{ Do the following repeatedly:

g.bg¯1 Draw a white background

g.circle 3⌿90 draw a circle of radius 90 at \$(90, 90)\$

g.ln a←90×1+z,2 1○t Line from \$(90,90)\$ to \$(90cos\theta, 90sin\theta)\$ for angle

g.rect a rectangle using the same coordinates

g.ln 90×1+z,(÷2○t),z,z,⍨÷1○t triangle with the points \$(90, 90),(90,90/cos\theta),(90/sin\theta,90)\$

t+←.1 increment angle \$\theta\$