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| 1 : | jj | 141 | #DESCRIPTION |
| 2 : | #KEYWORDS('Substitution' , 'Trig Substitution' , 'Trigonometric Substitution' ) | ||
| 3 : | #ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | |||
| 6 : | DOCUMENT(); # This should be the first executable line in the problem. | ||
| 7 : | |||
| 8 : | loadMacros( | ||
| 9 : | "PG.pl", | ||
| 10 : | "PGbasicmacros.pl", | ||
| 11 : | "PGchoicemacros.pl", | ||
| 12 : | "PGanswermacros.pl", | ||
| 13 : | "PGauxiliaryFunctions.pl", | ||
| 14 : | "PGasu.pl", | ||
| 15 : | "extraAnswerEvaluators.pl" | ||
| 16 : | ); | ||
| 17 : | |||
| 18 : | # No partial credit on this problem, so we say: | ||
| 19 : | install_problem_grader(~~&std_problem_grader); | ||
| 20 : | |||
| 21 : | TEXT(beginproblem()); | ||
| 22 : | $showPartialCorrectAnswers = 0; | ||
| 23 : | $pi = 4*atan2(1,1); | ||
| 24 : | @values =('\frac{1}{4}','\frac{3}{4}','\frac{1}{2}'); | ||
| 25 : | $tag1 = random(0,2,1); | ||
| 26 : | |||
| 27 : | |||
| 28 : | @sin_answers1 = (1/6, 1/3, 1/4); | ||
| 29 : | @sin_answers2 = (5/6, 2/3, 3/4); | ||
| 30 : | @sin_answers3 = (7/6, 4/3, 5/4); | ||
| 31 : | @sin_answers4 = (11/6, 5/3, 7/4); | ||
| 32 : | |||
| 33 : | |||
| 34 : | |||
| 35 : | TEXT(EV2(<<EOT)); | ||
| 36 : | Solve the following equation in the interval [0, 2 \(\pi \)]. | ||
| 37 : | $BR | ||
| 38 : | $BBOLD Note: $EBOLD | ||
| 39 : | Give the answer as a multiple of \( \pi \). | ||
| 40 : | Do not use decimal numbers. The answer should be a fraction or an integer. | ||
| 41 : | Note that \( \pi\) is already included in the answer so you just have to | ||
| 42 : | enter the appropriate multiple. E.g. if the answer is \( \pi/2 \) you should | ||
| 43 : | enter 1/2. If there is more than one answer enter them separated by commas. | ||
| 44 : | $PAR | ||
| 45 : | |||
| 46 : | \( (\sin(t))^2=$values[$tag1] \) | ||
| 47 : | $PAR | ||
| 48 : | t = \{ans_rule(30) \} \( \pi \) | ||
| 49 : | |||
| 50 : | EOT | ||
| 51 : | $ans1 = $sin_answers1[$tag1]; | ||
| 52 : | $ans2 = $sin_answers2[$tag1]; | ||
| 53 : | $ans3 = $sin_answers3[$tag1]; | ||
| 54 : | $ans4 = $sin_answers4[$tag1]; | ||
| 55 : | ANS(no_decimal_list("$ans1,$ans2,$ans3,$ans4")); | ||
| 56 : | |||
| 57 : | ENDDOCUMENT(); # This should be the last executable line | ||
| 58 : |
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