SmtC: Show me the Code!

< Hyperbola | Quadratic | Circle >

Circle

Equation: $(x - x_{0})^{2} + (y - y_{0})^{2} = r^{2}$
Parametrization: $\underset{―}{r} (t) = (\begin{matrix} x (t) \\ y (t) \end{matrix}) = r (\begin{matrix} \cos t \\ \sin t \end{matrix}), 0 \leq t < 2 π$
Unit vectors: $\underset{―}{e} = \underset{―}{e} (t) = (\begin{matrix} \cos t \\ \sin t \end{matrix}) = - \underset{―}{n}, \underset{―}{f} = \underset{―}{f} (t) = (\begin{matrix} - \sin t \\ \cos t \end{matrix}) = \underset{―}{t}$
Scalar Products: $\underset{―}{e} \cdot \underset{―}{e} = \underset{―}{f} \cdot \underset{―}{f} = 1, \underset{―}{e} \cdot \underset{―}{f} = 0$
Hat vectors: $\underset{―}{\hat{e}} = \underset{―}{f}, \underset{―}{\hat{f}} = - \underset{―}{e}$
Derivatives: ${\underset{―}{e}}^{'} = \underset{―}{f}, {\underset{―}{f}}^{'} = - \underset{―}{e}$

TiKZ Listing: Circle.tikz.tex. PDF PNG SVG ZIP*

\tikzmath{\R=3;}
\tikzmath{\RR=\R*1.2;}
\tikzmath{\AngleA=30;}
\tikzmath{\AngleB=75;}

\coordinate (O) at (0,0);
\coordinate (A) at (\AngleA:\R);
\coordinate (B) at (\AngleB:\R);

\draw (O) circle(\R);

\draw[-latex] (O) -- (0:\RR) node[right] {$x$};
\draw[-latex] (O) -- (90:\RR) node[above] {$y$};
\draw[-latex] (O) -- (A);
\draw[-latex] (O) -- (B);

\node at (\AngleA:\RR) {$\underline{e}(t_1)$};
\node at (\AngleB:\RR) {$\underline{e}(t_2)$};

\tkzMarkAngle(A,O,B);
\tkzLabelAngle[pos=1.5](A,O,B) {\small{$\theta=t_2-t_1$}};

θ = t_{2} - t_{1}

\cos θ = \underset{―}{e} (t_{1}) \cdot \underset{―}{e} (t_{2}) = (\begin{matrix} \cos t_{1} \\ \sin t_{1} \end{matrix}) \cdot (\begin{matrix} \cos t_{2} \\ \sin t_{2} \end{matrix})

Addition Formula:

\cos (t_{2} - t_{1}) = \cos t_{1} \cos t_{2} + \sin t_{1} \sin t_{2}

2_Palestras/2021/02_Curves/02_Quadratics/Images/Circles-001.svg

Generated: 31 Dec 1969, 20:59:59

100 of 100 images

Base Path: /usr/local/

Glob Path: Images/*.svg

TiKZ Listing: Circles.tikz.tex. PDF PNG SVG ZIP*

\tikzmath{\R=3;}
\tikzmath{\RR=\R*1.2;}
\tikzmath{\AngleA=30;}
\tikzmath{\AngleB=75;}

\coordinate (O) at (0,0);
\coordinate (e) at (\T:\R);
\coordinate (f) at (\T+90:\R);

\draw (O) circle(\R);

\draw[-latex] (O) -- (0:\RR) node[right] {$x$};
\draw[-latex] (O) -- (90:\RR) node[above] {$y$};
\draw[-latex] (O) -- (e);
\draw[-latex] (O) -- (f);

\node at (\T:\RR) {$\underline{e}$};
\node at (\T+90:\RR) {$\underline{f}$};

\tkzMarkRightAngle(e,O,f);

< Hyperbola | Quadratic | Circle >