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| 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 : |
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