# Tikz - Drawing in the unit circle

I am working on learning how to use tikz for mathematical drawings and I am currently trying to make... well... if you read or typeset the code you will get the idea.

If you look at the results the lines on either side of the y axis are not touching the top/bottom of the circle. However, I think they should (assuming I did my math right).

Any given point of the unit circle is (sin(\x),cos(\x)) I know cos(\x) is \x/8 thus sin(\x) is 1-\x/8*\x/8 (according to everyone fav trig identity).

Then when I draw a line, (\x/8,0) -- +(0,1-\x/8*\x/8) this should reach the top.

What am I doing wrong? Thanks for your time.

My Code:

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{backgrounds,calc}

\begin{document}
\begin{tikzpicture}[scale=3]
\coordinate [label=left:$O$] (O) at (0,0);
%Draw the Circle around it all
\draw[semithick] (0,0) circle (1);
%Draw lines to the top
\foreach \x in {-4,...,4}
\draw[red,very thick] (\x/8,0) -- +(0,1-\x/8*\x/8);
\end{tikzpicture}
\end{document}

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It is simply due to a forgotten square root step. It can be solved by adding sqrt.

\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=3]
\node[left] (O) at (0,0) {$O$};
%Draw the Circle around it all
\draw[semithick] (0,0) circle (1);
%Draw lines to the top
\foreach \x in {-4,...,4}
\draw[red,very thick] (\x/8,0) -- +(0,{sqrt(1-\x/8*\x/8)});
\end{tikzpicture}
\end{document}

-