Generate a Unit Circle Trigonometry

Question

Struggling often with Trigonometry I would like to have some code to generate this Unit Circle Trigonometry. Would be of great help when I need to transform some data :

Answer 1

There are a couple tricky points here. Here's a start, which I imagine you can finish.

markings[t_] := Module[{o={0,0},p={Cos[t],Sin[t]}, 
  t2=Together[t],tFormat, rot},
  tFormat = If[Denominator[t2]=!=1, 
    Row[{Numerator[t2],"/",Denominator[t2]}]];
  rot = If[TrueQ[Pi/2<Mod[t,2Pi]<3Pi/2],t+Pi,t];
    {{Opacity[0.3],Line[{o,p}]},
     Rotate[Inset[Style[
       Row[{t(180/Pi)Degree, " = ",tFormat}],
     FontSize->18], p/2],rot], 
     Text[{Cos[t],Sin[t]},p,-1.3p]}
];
Graphics[{
  Circle[{0,0},1],
  Table[markings[t],{t,{Pi/6,Pi/4,2Pi/3}}]
}]

In addition to finishing it, logical enhancements would include: Making the Circle thicker, adjusting the size and/or format of the point labels, adding Points on the boundary, and/or making it dynamic.

Have fun!

Answer 2

Here's a dynamic version (sorry, I couldn't resist).

Manipulate[
 DynamicModule[{alist, pt, pc},
  pt[a_] := {Cos[a], Sin[a]};
  alist = 
   Union[Range[0, 2 Pi - Pi/6, Pi/6], Range[0, 2 Pi - Pi/4, Pi/4]];
  a = Nearest[alist, Mod[ArcTan @@ p, 2 Pi, 0]][[1]];
  pc = pt[a];

  Graphics[{
    Circle[],
    {LightGray, Line[{{0, 0}, pt[#]}] & /@ alist},
    {PointSize[Medium], Blue, Point[pt /@ alist]},
    {AbsoluteThickness[2], Line[{{0, 0}, pc}]},
    {PointSize[Large], Red, Point[pc]},
    Text[pc, pc, -2 pc],
    Text[Framed[Row[{a/Pi/2 360, "\[Degree] = ", a}], 
      Background -> White, FrameStyle -> None], pc/2, {0, 0}, 
     pt[Mod[a, Pi, -Pi/2]]]},
   PlotRange -> {{-1.5, 1.5}, {-1.5, 1.5}}]],
 {{p, {1, 0}}, Locator, Appearance -> None},
 {{a, 0}, None}]