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| 1 : | jj | 61 | ## DESCRIPTION |
| 2 : | jjholt | 317 | ## Precalculus: Trigonometry |
| 3 : | jj | 61 | ## ENDDESCRIPTION |
| 4 : | |||
| 5 : | jjholt | 317 | ## KEYWORDS('precalculus','trigonometric graphs') |
| 6 : | ## Tagged by cmd6a 6/21/06 | ||
| 7 : | jj | 61 | |
| 8 : | jj | 318 | ## DBsubject('Trigonometry') |
| 9 : | jjholt | 483 | ## DBchapter('Trigonometric Functions of Real Numbers') |
| 10 : | jjholt | 317 | ## DBsection('Trigonometric Graphs') |
| 11 : | ## Date('') | ||
| 12 : | ## Author('') | ||
| 13 : | ## Institution('ASU') | ||
| 14 : | ## TitleText1('') | ||
| 15 : | ## EditionText1('') | ||
| 16 : | ## AuthorText1('') | ||
| 17 : | ## Section1('') | ||
| 18 : | ## Problem1('') | ||
| 19 : | jj | 61 | |
| 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 : | "PGasu.pl" | ||
| 29 : | ); | ||
| 30 : | |||
| 31 : | gage | 268 | TEXT(beginproblem()); |
| 32 : | jj | 61 | $showPartialCorrectAnswers = 1; |
| 33 : | |||
| 34 : | $a_n = random(2,15,1); | ||
| 35 : | $a_s = random(-1,1,2); | ||
| 36 : | $a = $a_n * $a_s; | ||
| 37 : | |||
| 38 : | $b = random(2,6,1); | ||
| 39 : | |||
| 40 : | $c_d = random(2,6,1); | ||
| 41 : | $c_s = random(-1,1,2); | ||
| 42 : | if ($c_s == -1) {$c_sign = '-'}; | ||
| 43 : | if ($c_s == 1) {$c_sign = '+'}; | ||
| 44 : | |||
| 45 : | BEGIN_TEXT | ||
| 46 : | Let \( y = $a \cos\left($b (x $c_sign \frac { \pi } { $c_d } )\right) \). | ||
| 47 : | $BR$BR | ||
| 48 : | What is the amplitude? \{ ans_rule(15) \} | ||
| 49 : | $BR$BR | ||
| 50 : | What is the period? \{ ans_rule(15) \} | ||
| 51 : | $BR$BR | ||
| 52 : | END_TEXT | ||
| 53 : | |||
| 54 : | # For the phase shift, is the graph shifted $BITALIC left $EITALIC | ||
| 55 : | # or $BITALIC right $EITALIC? \{ ans_rule(15) \} | ||
| 56 : | BEGIN_TEXT | ||
| 57 : | For the phase shift, which way is the graph shifted? | ||
| 58 : | \{ pop_up_list('?' => ' ? ', 'Left' => 'Left', 'Right' => 'Right') \} | ||
| 59 : | $BR$BR | ||
| 60 : | How far is it shifted? \{ ans_rule(15) \} | ||
| 61 : | $BR$BR | ||
| 62 : | [NOTE: If needed, you can enter \(\pi\) as 'pi' in your answers.] | ||
| 63 : | |||
| 64 : | END_TEXT | ||
| 65 : | |||
| 66 : | $dir = "left"; | ||
| 67 : | $dir = "right" if($c_s < 0); | ||
| 68 : | # record the answers | ||
| 69 : | ANS(num_cmp($a_n)); | ||
| 70 : | ANS(num_cmp("2 * pi / $b")); | ||
| 71 : | ANS(str_cmp($dir)); | ||
| 72 : | ANS(num_cmp("pi/$c_d")); | ||
| 73 : | |||
| 74 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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