Drawing a triangle, with angles inside, inside a circle and other details

Question

I am trying to draw a figure similar to this one

This is the code for that figure that I've done so far

\documentclass{article}
\usepackage[utf8]{inputenc}

\usepackage{tikz}
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{xcolor}

\begin{document}

\begin{tikzpicture}
    %coordinate system
    \draw[thick,->] (0,-5) -- (0,5)node[above left]{$y$};
    \draw[thick,->] (-5,0) -- (5,0)node[below right]{$x$};
    
%circle
\draw (4,0) arc (0:360:4)node[ below]{$ $};

%dots % their lines
\draw[red] (0,0) -- (2.8,2.9)  node[circle,red,fill,inner sep=3pt]{} node[above right]{$Q=(\cos v,\sin v)$};

\draw[blue] (0,0) -- (-2.8,2.9)  node[circle,blue,fill,inner sep=3pt]{} node[above left]{$P=(\cos u,\sin u)$};

%line joining both dots
\draw[magenta] (-2.8,2.9) -- (2.8,2.9) node[midway, above left ]{$d$};

%angles
\draw (2,0) arc (0:134:2)node[midway,above right]{$u $};

\draw (1,0) arc (0:45:1)node[midway,above right]{$v $};

\end{tikzpicture}

\end{document}

How can I draw the arrows for the direction of the angles?

And also how can I add the label for the circle, it's supposed to be a unit circle, I wanted to draw an arrow indicating that the equation $x^2+y^2=1$ is that circle.

Could someone please help?

Thank you in advance.

Edit.

The label for the circle without arrow: %circle \draw (4,0) arc (0:360:4)node[very near end, below right]{$x^2+y^2=1$};

Edit2.

So far, the image is this, which looks decent :) I think.

Answer 1

Arrow tips for arcs are added the same way as arrow tips to other paths, so do exactly the same as you did for the axes: [->]

For the equation: add the node with e.g. \node (eq) at (x,y) {...}; with suitable values for x and y, or \node (eq) at (angle:radius) {...}; to use polar coordinates instead of Cartesian coordinates. Having named the node eq, you can draw an arrow from it to the circle with e.g. \draw [->] (eq) -- (-20:4);, again using polar coordinates.

In the code below I used polar coordinates to place the P and Q nodes as well, and included a style for the dots, and used labels for the P/Q labels. Obviously your method with a second node works fine as well, so this is mostly a matter of personal preference I guess. Polar coordinates are quite convenient in this case though. Oh, and I used the circle construct to make the circle instead of an arc.

\documentclass{article}%
\usepackage[utf8]{inputenc}

\usepackage{tikz}

\begin{document}

\begin{tikzpicture}[dot/.style={circle,fill,inner sep=3pt, outer sep=0}]

%coordinate system
\draw[thick,->] (0,-5) -- (0,5) node[above left]{$y$};
\draw[thick,->] (-5,0) -- (5,0) node[below right]{$x$};
    
%circle
\draw (0,0) circle[radius=4cm];

%dots 
\path [red]  (45:4)  node[dot, label={above right:{$Q=(\cos v,\sin v)$}}] (p) {};
\path [blue] (135:4) node[dot, label={above left:{$P=(\cos u,\sin u)$}}] (q) {};

%line joining dots
\draw[magenta] (p) -- (q) node[midway, above left ]{$d$};
\draw [red]    (0,0) -- (p);
\draw [blue]   (0,0) -- (q);

%angles
\draw [->] (2,0) arc (0:135:2) node[midway,above right] {$u$};
\draw [->] (1,0) arc (0:45:1)  node[midway,above right] {$v$};

\node (eq) at (-10:6cm) {$x^2 + y^2 = 1$};    
\draw [->] (eq) to[bend left] (-30:4);

\end{tikzpicture}

\end{document}