PolarGraph

DOCUMENT();

loadMacros('PGstandard.pl', 'PGML.pl', 'PGtikz.pl', 'PGcourse.pl');

Preamble

We use PGtikz.pl to generate the graph.

Context()->variables->are(t => 'Real');

$graph = createTikZImage();
$graph->tikzLibraries('arrows.meta');
$graph->BEGIN_TIKZ
\tikzset{>={Stealth[scale=1.5]}}
\filldraw[
    draw=LightBlue,
    fill=white,
    rounded corners=10pt,
    thick,use as bounding box
] (-3.5,-3.5) rectangle (3.5,3.5);
\draw[->] (-3.5,0) -- (3.5,0) node[above left,outer sep=3pt] {\(x\)};
\draw[->] (0,-3.5) -- (0,3.5) node[below right,outer sep=3pt] {\(y\)};
\draw[DarkGreen,very thick]
    plot [samples=250,domain=0:{2*pi},variable=\t]
    ({3*cos(5*\t r)*cos(\t r)},{3*cos(5*\t r)*sin(\t r)});
\fill[opacity=0.5,fill=DarkGreen]
    (0,0) -- plot[samples=250,domain={-pi/10}:{pi/10},variable=\t]
    ({3*cos(5*\t r)*cos(\t r)},{3*cos(5*\t r)*sin(\t r)}) -- cycle;
END_TIKZ

BEGIN_PGML
Find the area enclosed by one petal of the rose curve
[`r = f(\theta) = \cos(5\theta)`].

>>[@ image($graph, width => 300) @]*<<

>>Graph of [`r = \cos(5\theta)`]<<

Area = [_____]{'pi/20'}
END_PGML

Setup

The package PGtikz.pl is used to produce the curve. The plotting routine used in this way plots parametrically and we plot the polar curve parametrically.

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.

Polar Graph

Complete Code

POD for Macro Files

PG problem file

Explanation