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# Annotation of /trunk/NationalProblemLibrary/Rochester/setDerivatives4Trig/s2_4_27a.pg

 1 : jj 145 ##DESCRIPTION 2 : ##KEYWORDS('derivatives', 'trigonometry', 'product rule') 3 : ## Find a derivative of a function involving trigonometric functions, 4 : ## and evalute it at a given point; requires using product rule 5 : ##ENDDESCRIPTION 6 : 7 : jjholt 184 ## Tagged by sawblade 8 : 9 : ## DBsubject('Calculus') 10 : ## DBchapter('Differentiation') 11 : ## DBsection('Derivatives of Trigonometric Functions') 12 : ## Date('') 13 : ## Author('') 14 : ## Institution('Rochester') 15 : ## TitleText1('') 16 : ## EditionText1('') 17 : ## AuthorText1('') 18 : ## Section1('') 19 : ## Problem1('') 20 : sh002i 556 ## TitleText2('Calculus: Early Transcendentals') 21 : ## EditionText2('1') 22 : ## AuthorText2('Rogawski') 23 : ## Section2('3.6') 24 : ## Problem2('15') 25 : jjholt 184 26 : jj 145 DOCUMENT(); # This should be the first executable line in the problem. 27 : 28 : loadMacros( 29 : "PG.pl", 30 : "PGbasicmacros.pl", 31 : "PGchoicemacros.pl", 32 : "PGanswermacros.pl", 33 : "PGauxiliaryFunctions.pl" 34 : ); 35 : 36 : TEXT(beginproblem()); 37 : $showPartialCorrectAnswers = 1; 38 : 39 :$pi = arccos(-1); 40 : 41 : $a_n = random(2,12,1); 42 :$a_s = random(-1,1,2); 43 : $a =$a_n * $a_s; 44 : 45 :$x_d = random(3,6,1); 46 : while ($x_d == 5) {$x_d = random(3,6,1);}; 47 : 48 : $q = random(0,1,1); 49 : if ($q == 0) { 50 : $x_n = 1; 51 :$x_s = -1; 52 : $x_sign = '-'; 53 : }; 54 : if ($q == 1) { 55 : $x_n = 1; 56 :$x_s = 1; 57 : $x_sign = ''; 58 : }; 59 : if ($q == 2) { 60 : $x_n =$x_d - 1; 61 : $x_s = 1; 62 :$x_sign = ''; 63 : }; 64 : if ($q == 3) { 65 :$x_n = $x_d + 1; 66 :$x_s = 1; 67 : $x_sign = ''; 68 : }; 69 : if ($q == 4) { 70 : $x_n = 2 *$x_d - 1; 71 : $x_s = 1; 72 :$x_sign = ''; 73 : }; 74 : 75 : if ($x_n != 1) {$x_num = $x_n }; 76 : if ($x_n == 1) { $x_num = '' }; 77 : 78 :$x = $x_s*$x_n*$pi/$x_d; 79 : 80 : $deriv1 =($a*(sin($x)+cos($x))+ $a*$x*(cos($x)-sin($x))); 81 : $funct1 ="($a*(sin(x)+cos(x))+ \$a*x*(cos(x)-sin(x)))"; 82 : 83 : TEXT(EV2(<