##DESCRIPTION
#  Created: 3/2/02
#  Authors: Minock
#  Stewart 4th ed. Section 10.2
#  Find d2y/dx2 for parametric equations.
##ENDDESCRIPTION

##KEYWORDS('parametric')
## tcao tagged and PAID on 12-12-2003

## DBchapter('Parametric Equations and Polar Coordinates')
## DBsection('Tangents and Areas')
## Date('6/3/2002')
## Author('')
## Institution('')
## TitleText1('Calculus Early Transcendentals')
## EditionText1('4')
## AuthorText1('Stewart')
## Section1('10.2')
## Problem1('15')
DOCUMENT();

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

TEXT(&beginproblem);
$showPartialCorrectAnswers = 1;

$a = random(1,9,1);
$b = random(2,9,1);
$c = random(1,9,1);
$d = random(2,5,1);
$ans = "($d*($d-1)/($b**2))(cos(t)**($d-2))";

$NO_SPACE = '@{\,}';

BEGIN_TEXT

Find \( \displaystyle \frac{d^2y}{dx^2} \), as a fuction of \(t\), for 
the given the parametric equations:
\[ \begin{array}{r${NO_SPACE}c${NO_SPACE}l}
x & = & $a - $b \cos(t) \cr
y & = & $c + \cos^{$d}(t) 
\end{array} \]
\( \displaystyle \frac{d^2y}{dx^2} = \) \{ ans_rule(50) \}.

END_TEXT
&ANS(function_cmp($ans, "t"));

ENDDOCUMENT();