Using Special Trig Values on the Unit Circle

Displays values of trig functions on the unit circle

Complete Code

POD for Macro Files

specialTrigValues.pl

PG problem file

Explanation

DOCUMENT();

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

Preamble

We load the specialTrigValues.pl macro to use exact values on the unit circle.

($d, $n) = random_coprime([ 2, 3, 4, 6 ], [ 1 .. 12 ]);

$r = random(2, 3);

$c = specialRadical("$r cos($n pi/$d)");
$s = specialRadical("$r sin($n pi/$d)");

$x = list_random(sqrt(3) / 2, sqrt(2) / 2, 1 / 2);
$a = specialAngle(arcsin($x));

Context("Complex");
$z = specialRadical("$r exp($n pi i/$d)");

Setup

The random_coprime function selects two random numbers that are coprime from the list. This will give fractions with denominators of 2,3,4 or 6.

The specialRadical function returns a MathObject in the form a sqrt(b)/c were b, c come from a list of integers (defaults to [1,2,3]).

It is noted that specialRadical has a complex form as well.

The specialAngle function returns a MathObject in the form a pi/c where a in an integer and c comes from a list (defaults to [1,2,3,4,6]).

BEGIN_PGML
Evaluate the following:

a) [`[$r] \cos([$n] \pi/[$d])=`] [_]{$c}

b) [`[$r] \sin([$n] \pi/[$d])=`] [_]{$s}

c) [`[$r] \exp([$n] \pi/[$d])=`] [_]{$z}

d) [`\arcsin([$x])=`] [_]{$a}
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.