Simpler Diagram for Trigonometric Functions With Unit Circle


In my previous post about unit circle and trigonometric functions, I included a graph with three trigonometry functions. I’m quite satisfied with my TikZ picture.


Unluckily, a secondary school student found that my diagram was too complicated.


\newcommand\mytheta{110} %angle theta
\coordinate[label=left:$O$] (O) at (0,0);
\coordinate[label=above left:${A = (\cos\theta, \sin\theta)}$] (A) at (\mytheta:1);
\coordinate[label=below left:${B = (\cos(-\theta), \sin(-\theta))}$] (B) at (-\mytheta:1);
\coordinate[label=right:$E$] (E) at (1,0);
\draw (O) circle (1);
\draw (A) -- (O)  node [midway, left] {$1$}
    -- (E);
\draw (B) -- (O);
\draw[-stealth] ($(O)!0.3!(E)$) arc (0:\mytheta:0.3) node[midway, above] {$\theta$};
\draw[-stealth] ($(O)!0.25!(E)$) arc (0:{-\mytheta}:0.25) node[midway, below] {$-\theta$};

unit circle sine cosine

Skills learnt:

  • \coordinate[label=above left:$O$] (O) at (0,0); for labelling a point.
  • Inside the $...$, if I put A = (\cos \theta, \sin \theta), the system will complain. We have to surround this with a pair of curly braces ${...}$.
  • To produce the convex combination of two points ($(O)!.3!(E)$), we have to wrap the whole expression with a pair of parenthesis.

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