Kurva Parametrik #3

Ini adalah tiga contoh terakhir dari kurva parametrik, setelah yang ini dan yang itu. Semuanya saya susun (compile) dalam jaringan melalui Online LaTeX Editor ShareLaTeX.

Demikian semoga bermanfaat.

Adjie Gumarang Pujakelana 2014 

Contoh 7

\documentclass[a4paper,10pt]{standalone}
\usepackage[T1]{fontenc}
\usepackage{concmath,gentium}
\usepackage[svgnames]{xcolor}
\setlength{\parindent}{0pt}
\usepackage{fix-cm}
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{tikz}

\begin{document}

\color{MidnightBlue}
\centering
\begin{tikzpicture}[-latex,scale=2.15]

% Draw the lines at multiples of pi/12
\foreach \ang in {0,...,31} {
  \draw [lightgray] (0,0) -- (\ang * 180 / 16:4);
}

% Concentric circles and radius labels
\foreach \s in {0, 1, 2, 3} {
  \draw [lightgray] (0,0) circle (\s + 0.5);
  \draw (0,0) circle (\s);
  \node [fill=white] at (\s, 0) [below] {\scriptsize $\s$};
}

% Add the labels at multiples of pi/4
\foreach \ang/\lab/\dir in {
  0/0/right,
  1/{\pi/4}/{above right},
  2/{\pi/2}/above,
  3/{3\pi/4}/{above left},
  4/{\pi}/left,
  5/{5\pi/4}/{below left},
  7/{7\pi/4}/{below right},
  6/{3\pi/2}/below} {
  \draw (0,0) -- (\ang * 180 / 4:4.1);
  \node [fill=white] at (\ang * 180 / 4:4.2) [\dir] {\scriptsize $\lab$};
}

% The double-lined circle around the whole diagram
\draw [style=double] (0,0) circle (4);

\fill [fill=red!50!black, opacity=0.5] plot [domain=-pi/2:pi/2] (xy polar cs:angle=\x r,radius= {2-2*sin(\x r)});
\draw [thick,color=red,domain=0:2*pi,samples=200,smooth] plot (xy polar cs:angle=\x r,radius= {2-2*sin(\x r)});
\node [fill=white] at (2,1) {$r=2-2\sin\theta$};
\end{tikzpicture} 

\end{document}

Contoh 8

\documentclass[a4paper,10pt]{standalone}
\usepackage[T1]{fontenc}
\usepackage{concmath,gentium}
\usepackage[svgnames]{xcolor}
\setlength{\parindent}{0pt}
\usepackage{fix-cm}
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{tikz}

\begin{document}

\color{MidnightBlue}
\centering
\begin{tikzpicture}[-latex,scale=2.15]
\fill [fill=Tomato, opacity=0.75] plot [domain=-pi/2:pi/2] (xy polar cs:angle=\x r,radius= {2-2*sin(\x r)});
\draw [thick,color=Tomato,domain=0:2*pi,samples=200,smooth] plot (xy polar cs:angle=\x r,radius= {2-2*sin(\x r)});
\node [fill=white] at (0,0.75) {\fontsize{.5cm}{1.95cm}\selectfont$r=2-2\sin\theta$};
\end{tikzpicture} 

\end{document}

Contoh 9

\documentclass[a4paper,10pt]{standalone}
\usepackage[T1]{fontenc}
\usepackage{concmath,gentium}
\usepackage[svgnames]{xcolor}
\setlength{\parindent}{0pt}
\usepackage{fix-cm}
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{pgfplots}
\pgfplotsset{compat=1.9}
    \usepgfplotslibrary{polar}
    \usepgfplotslibrary{units}
\pgfplotsset{every axis/.append style={
                    axis x line=middle,    % put the x axis in the middle
                    axis y line=middle,    % put the y axis in the middle
                    axis line style={<->,color=blue}, % arrows on the axis
                    xlabel={$x$},          % default put x on x-axis
                    ylabel={$y$},          % default put y on y-axis
            }}

\begin{document}

\color{MidnightBlue}
\centering
\begin{tikzpicture}[scale=2.5]
\begin{axis}[
    domain=-pi/2:pi/2, % The range over which to evaluate the functions
    xtick={-1,...,1}, ytick={-1,...,1}, % Tick marks only on integers between -1 and 1
    axis lines=middle, % Axis lines go through (0,0)
    enlargelimits=true, % Make the axis lines a bit longer than required for the plots
    samples=101, % Number of samples for evaluating the functions (use an odd number to capture the (0,0) point
    xlabel=$x$, ylabel=$y$, % Axis labels
    clip=false % So the labels aren't cut off
]
\addplot [thick, IndianRed]
    ( {sqrt(2) * sin(deg(x))},
      {abs(sin(deg(x*2)))} )
    node [pos=0.8, anchor=south] {$f(x) = |x|\sqrt{2-x^2}$}; % Add a text node at 80% of the plot length
\addplot [thick, SeaGreen]
    ( {sqrt(2) * sin(deg(x))},
      {-abs(sin(deg(x*2)))} )
    node [pos=0.8, anchor=north] {$f(x) = -|x|\sqrt{2-x^2}$};
\end{axis}
\end{tikzpicture}

\end{document}