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# Annotation of /trunk/NationalProblemLibrary/ASU-topics/setTrigGraphs/p23.pg

 1 : jj 61 ## DESCRIPTION 2 : ## Geometry: Plane Geometry 3 : ## ENDDESCRIPTION 4 : 5 : ## KEYWORDS('geometry', 'plane') 6 : ## Tagged by YJ 7 : 8 : ## DBsubject('Geometry') 9 : ## DBchapter('Plane Geometry') 10 : ## DBsection('Trigonometric Functions') 11 : ## Date('5/26/2005') 12 : ## Author('Jeff Holt') 13 : ## Institution('UVA') 14 : ## TitleText1('Calculus') 15 : ## EditionText1('5e') 16 : ## AuthorText1('Stewart') 17 : ## Section1('5.8.2') 18 : ## Problem1(' ') 19 : 20 : DOCUMENT(); # This should be the first executable line in the problem. 21 : 22 : loadMacros( 23 : "PG.pl", 24 : "PGbasicmacros.pl", 25 : "PGchoicemacros.pl", 26 : "PGanswermacros.pl", 27 : "PGauxiliaryFunctions.pl", 28 : "PGgraphmacros.pl", 29 : "PGasu.pl" 30 : ); 31 : 32 : TEXT(&beginproblem); 33 : 34 : $a=random(-4, -1); 35 : 36 :$c=random(1, 8); 37 : $b=1/$c; 38 : $pi=4*arctan(1); 39 :$xdom=3*$c; 40 :$ydom=abs($a)+1; 41 :$xgrid=2*$xdom; 42 :$ygrid=2*$ydom; 43 :$graph = init_graph(-$xdom,-$ydom,$xdom,$ydom,'axes'=>[0,0],'grid'=>[$xgrid,$ygrid]); 44 : $f = FEQ("$a*cos($pi*$b*x) for x in <-$xdom,$xdom> using color:blue and weight:2"); 45 : ($fref) = plot_functions($graph, $f); 46 :$period = 2*$c; 47 : 48 : # Label some points 49 :$label1 = new Label(0,$a, "$a",'black','right'); 50 : $d = -$a; 51 : $label2 = new Label($c, $d, "($c,$d)",'black','bottom','center'); 52 :$label3 = new Label(0,$d,"$d",'black','top'); 53 : $graph->lb($label1, $label2,$label3); 54 : 55 : 56 : BEGIN_TEXT 57 : \{ image(insertGraph($graph)) \}$PAR 58 : To get a better look at the graph, you can click on it. 59 : $PAR 60 : 61 : 62 : The curve above is the graph of a sinusoidal function. It goes through 63 : the point $$(c,d)$$. 64 : Find a sinusoidal function that matches the given graph. If needed, you can enter 65 : $$\pi$$=3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits. 66 :$PAR 67 : $$f(x) =$$ \{ans_rule(60)\} 68 : END_TEXT 69 : 70 : # 71 : # Tell WeBWork how to test if answers are right. These should come in the 72 : # same order as the answer blanks above. You tell WeBWork both the type of 73 : # "answer evaluator" to use, and the correct answer. 74 : # 75 : $ans = "$a*cos($pi*$b*x)"; 76 : 77 : &ANS(function_cmp($ans,"x",-$xdom,\$xdom)); 78 : 79 : ENDDOCUMENT(); # This should be the last executable line in the problem. 80 :