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I am trying to draw this picture


I tried
	\begin{tikzpicture}[declare function={r=1;myangle=30;},c/.style={circle,fill,inner sep=1pt},>=latex,scale=2]
		(0,0) coordinate (O)	
		(myangle:r) coordinate (M)
		(180-myangle:r) coordinate (M')
		\draw[->] (-1.5,0) -- (1.5,0) node[below] {$x$};
		\draw[->] (0,-1.5) -- (0,1.5) node[right] {$y$};
		% draw the unit circle
		\draw[thick] (0,0) circle[radius=1];
		(M') -- (M) ;
		\draw (0,0) -- (M) (0,0) -- (M');
		\path foreach \p/\g in {O/-45,M/90,M'/90}{(\p)node[c]{}+(\g:1.8mm) node{$\p$}};

I get 
Top Answer
I propose the following that uses:

- the `-|` binary operator to compute coordinates;

- the `angles` Ti*k*Z library for angle markings, and;

- the `quotes` Ti*k*Z library for convenience.

I removed the `scale=2` setting because it would make the circle `radius` and the `angle radius` of the angle markings inconsistent (the latter wouldn't be scaled). Of course, I adapted the coordinates accordingly.

I also colored the 𝛼 angle label in the same color (blue) as the corresponding arrow for clarity.

\usetikzlibrary{angles, quotes}
  declare function={r=2cm; myangle=30; ax=1.3*r;},
  c/.style={circle, fill, inner sep=1pt},
  \path       (0,0) coordinate (O)
        (myangle:r) coordinate (M)
    (180-myangle:r) coordinate (M')
    (O -| M')       coordinate (K)
    (O -| M)        coordinate (H);

  \draw[->] (-ax,0) -- (ax,0) node[below] {$x$};
  \draw[->] (0,-ax) -- (0,ax) node[right] {$y$};

  % The unit circle
  \draw[thick] (0,0) circle[radius=r];

  \draw[dashed] (K) -- (M') -- (M) -- (H);
  \draw (M') -- (O) -- (M);
  \path foreach \p/\g in {O/-45, M/45, M'/135, K/-90, H/-90} {
    (\p) node[c] {} +(\g:0.15*r) node{$\p$}

  % The angle arrows and labels
    pic ["$\alpha$" blue, draw=blue, angle radius=0.25*r,
         angle eccentricity=1.4] {angle = H--O--M}
    pic ["$\pi - \alpha$", draw, angle radius=0.46*r,
         angle eccentricity=0.68] {angle = H--O--M'};


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