Polar Graph (plots)

Graphing a polar curve given by r = f(theta)

Complete Code

POD for Macro Files

plots.pl

PG problem file

Explanation

DOCUMENT();

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

Preamble

The plots.pl macro is used to generate the graph.

$plot = Plot(
    xmin        => -2.2,
    xmax        =>  2.2,
    ymin        => -2.2,
    ymax        =>  2.2,
    xtick_delta =>  0.5,
    ytick_delta =>  0.5,
    xlabel      => '\(x\)',
    ylabel      => '\(y\)',
);

$plot->add_function(
    '2cos(5t)', 't', '-pi/10', 'pi/10',
    fill  => 'self',
    polar => 1,
    color => 'blue'
);
$plot->add_function('2cos(5t)', 't', 0, 'pi', polar => 1, color => 'blue');

Setup

The plot is set up with the Plot object and the plotting window.

The function is added with add_function and in this case the polar => 1 is required to plot the function in polar coordinates. The first add_function does the shading of one of the petals. The second one plots the remainder of the curve.

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

>>[!a rose curve with five petals!]{$plot}{400}<<

>>Graph of [`r = 2\cos(5\theta)`]<<

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

Statement

This is the problem statement in PGML.

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.