Question

I want to draw a trigonometric circle to represent a negative angle and defined a negative polar coordinate like \tkzDefPoint(-60:1){Q} to draw an arc, arc label and a sector on it. Given that the angle value is negative(-60), I expected the commands \tkzDrawArc and \tkzDrawSector to be drawn clockwise, but they were drawn in its default direction, counterclockwise. Even the position of the arc label drawn by \tkzLabelArc is far from the arc and appears to be positioned counterclockwise. How can I change the direction of drawing the arc, arc label and sector from counterclockwise to clockwise?? I tried using the reverse option but it didn't work.

\documentclass{standalone}
\usepackage{tikz,tkz-euclide}
\begin{document}

\begin{tikzpicture}
  \tkzDefPoint(0,0){O}
  \tkzDefPoint(1,0){A}
  \tkzDefPoint(-60:1){Q}

  \tkzDrawCircle[draw=black](O,A)

  \tkzDrawSector[R with nodes,fill=blue,line width=0.2pt](O,1)(A,Q)

  \tkzDrawSegment[thin](O,Q)

  \tkzDrawPoint[fill=black](Q)
  \tkzDrawPoint[fill=black](A)
  \draw[-{Stealth}] (-1.5,0) -- (1.5,0) node[right,xshift=-3pt] {\tiny$x$};
  \draw[-{Stealth}] (0,-1.5) -- (0,1.5) node[above,yshift=-3pt] {\tiny$y$};

  \tkzLabelPoint[below](Q){\tiny$Q$}
  \tkzLabelPoint[below left](O){\tiny$O$}
  \tkzLabelPoint[above right](A){\tiny$A$}

  \tkzDrawArc[-{Stealth}, line width=1pt](O,A)(Q)
\tkzLabelArc[below right](O,A,Q){$-$}
\end{tikzpicture}
\end{document}

The image below shows what I want:

Answer 1

Note added, following discussion in comments, etc:

This library has various commands that draw or use arcs, here you use the DrawSector, DrawArc, LabelArc. Each of these commands takes a sequence of arguments {o, S, T}: an origin, a Start S, and an end T.

• The library considers the arc as going "from" S "to" T, anticlockwise
• It seems that you would like to consider the arc as:
  • counting "up" (anticlockwise) from S to T if T > S
  • counting "down" (backwards, clockwise) if T < S

I can't see any obvious pitfalls in implementing a library with your preferred logic, but it's not how this library works, and no amount of rephrasing your question will change that.

You could perhaps write wrapper functions that test S > T and pass the arguments on to the library commands in the appropriate order, e.g. myDrawArc, but you would need some care in reversing optional arguments -- in this example, we have an arrow that needs to be reversed; what if you had, say, some fancy shading on the sector fill? (i.e. I think it would be potentially complicated and messy, rather than the "cleaner" code you are looking for, but you can consider whether it would work in your use case.)

my answer below aims to demonstrate how the library's logic works, by swapping the order of S and T (your Q and A), and how (or one possible way) to get a "clockwise" arrow on an "anticlockwise" arc. I showed the switch for the DrawArc and LabelArc but I didn't do it for DrawSector (based on your original picture). But of course you can do that as well, as shown in Sebastiano's answer.

===== earlier answer ===

Think of the arc syntax as going "from" a to b, anticlockwise. So draw the arc "from" Q to A. Then reverse the arrow. Edit: seems you also want "from Q to A" for the label.

\tkzDrawArc[-{Stealth}, line width=1pt,reverse](O,Q)(A)
\tkzLabelArc[below right](O,Q,A){$-$}

\documentclass{standalone}
\usepackage{tikz,tkz-euclide}
\begin{document}

\begin{tikzpicture}
  \tkzDefPoint(0,0){O}
  \tkzDefPoint(1,0){A}
  \tkzDefPoint(-60:1){Q}

  \tkzDrawCircle[draw=black](O,A)

  \tkzDrawSector[R with nodes,fill=blue,line width=0.2pt](O,1)(A,Q)

  \tkzDrawSegment[thin](O,Q)

  \tkzDrawPoint[fill=black](Q)
  \tkzDrawPoint[fill=black](A)
  \draw[-{Stealth}] (-1.5,0) -- (1.5,0) node[right,xshift=-3pt] {\tiny$x$};
  \draw[-{Stealth}] (0,-1.5) -- (0,1.5) node[above,yshift=-3pt] {\tiny$y$};

  \tkzLabelPoint[below](Q){\tiny$Q$}
  \tkzLabelPoint[below left](O){\tiny$O$}
  \tkzLabelPoint[above right](A){\tiny$A$}

  \tkzDrawArc[-{Stealth}, line width=1pt,reverse](O,Q)(A)
\tkzLabelArc[below right](O,Q,A){$-$}
\end{tikzpicture}
\end{document}

Answer 2

Some thing like this?

    \documentclass{article}
    \usepackage{tikz}
    \usepackage{tkz-euclide}
    \usetikzlibrary{arrows.meta}
    \begin{document}
    
    \begin{tikzpicture}
    \tkzDefPoint(0,0){O}
    \tkzDefPoint(1,0){A}         
    \tkzDefPoint(-60:1){Q}
    \tkzDrawCircle[draw=black](O,A)
    \tkzDrawSector[R with nodes, fill=blue!20, line width=0.2pt](O,1)(Q,A)
    \tkzDrawSegment[thin](O,Q)
    
    \tkzDrawPoint[fill=black](Q)
    \tkzDrawPoint[fill=black](A)
    \draw[-{Stealth}] (-1.5,0) -- (1.5,0) node[right,xshift=-3pt] {\tiny$x$};
    \draw[-{Stealth}] (0,-1.5) -- (0,1.5) node[above,yshift=-3pt] {\tiny$y$};
    
    \tkzLabelPoint[below](Q){\tiny$Q$}
    \tkzLabelPoint[below left](O){\tiny$O$}
    \tkzLabelPoint[above right](A){\tiny$A$}
    
    \tkzDrawArc[{Stealth}-, line width=1pt](O,Q)(A)
    \end{tikzpicture}
    
    \end{document}

Addendum: using \tkzLabelArc[pos=0.5, shift={(-.1,3pt)}](O,A,Q){$-$}

\documentclass{article}
\usepackage{tikz}
\usepackage{tkz-euclide}
\usetikzlibrary{arrows.meta}
\begin{document}

\begin{tikzpicture}
  \tkzDefPoint(0,0){O}
  \tkzDefPoint(1,0){A}         
  \tkzDefPoint(-60:1){Q}
  
  \tkzDrawCircle[draw=black](O,A)
  
  % (clockwise sector)
  \tkzDrawSector[R with nodes, fill=blue!20, line width=0.2pt](O,1)(Q,A)
  
  % A -> Q (complement)
  \tkzDrawSector[R with nodes, fill=orange!20, line width=0.2pt](O,1)(A,Q)
  
  \tkzDrawSegment[thin](O,Q)
  
  \tkzDrawPoint[fill=black](Q)
  \tkzDrawPoint[fill=black](A)
  
  \draw[-{Stealth}] (-1.5,0) -- (1.5,0) node[right,xshift=-3pt] {\tiny $x$};
  \draw[-{Stealth}] (0,-1.5) -- (0,1.5) node[above,yshift=-3pt] {\tiny $y$};
  
  \tkzLabelPoint[below](Q){\tiny $Q$}
  \tkzLabelPoint[below left](O){\tiny $O$}
  \tkzLabelPoint[above right](A){\tiny $A$}
  
 \tkzLabelArc[pos=0.5, shift={(-.1,3pt)}](O,A,Q){$-$}
\tkzDrawArc[{Stealth}-, line width=1pt](O,Q)(A)
\end{tikzpicture}

\end{document}