// Numbas version: exam_results_page_options
{"name": "Exact values for sin, cos, tan (acute, radians)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/exact_values_radians_We6EFEi.svg", "/srv/numbas/media/question-resources/exact_values_radians_We6EFEi.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"js": "", "css": ""}, "showQuestionGroupNames": false, "parts": [{"prompt": "<p>The exact value of $\\sin\\Large($$\\var{distheta}\\Large)$ is</p>", "maxMarks": 0, "choices": ["<p>$\\dfrac{1}{2}$</p>", "<p>$\\dfrac{1}{\\sqrt{2}}$</p>", "<p>$\\dfrac{\\sqrt{3}}{2}$</p>", "<p>$\\dfrac{1}{\\sqrt{3}}$</p>", "<p>$\\sqrt{3}$</p>", "<p>$1$</p>"], "displayType": "radiogroup", "displayColumns": 0, "distractors": ["", "", "", "", "", ""], "variableReplacementStrategy": "originalfirst", "minMarks": 0, "shuffleChoices": true, "variableReplacements": [], "type": "1_n_2", "matrix": ["if(theta=30,1,0)", "if(theta=45,1,0)", "if(theta=60,1,0)", 0, 0, 0], "scripts": {}, "showCorrectAnswer": true, "marks": 0}, {"prompt": "<p>The exact value of $\\cos\\Large($$\\var{distheta}\\Large)$&nbsp;is</p>", "maxMarks": 0, "choices": ["<p>$\\dfrac{1}{2}$</p>", "<p>$\\dfrac{1}{\\sqrt{2}}$</p>", "<p>$\\dfrac{\\sqrt{3}}{2}$</p>", "<p>$\\dfrac{1}{\\sqrt{3}}$</p>", "<p>$\\sqrt{3}$</p>", "<p>$1$</p>"], "displayType": "radiogroup", "displayColumns": 0, "distractors": ["", "", "", "", "", ""], "variableReplacementStrategy": "originalfirst", "minMarks": 0, "shuffleChoices": true, "variableReplacements": [], "type": "1_n_2", "matrix": ["if(theta=60,1,0)", "if(theta=45,1,0)", "if(theta=30,1,0)", 0, 0, 0], "scripts": {}, "showCorrectAnswer": true, "marks": 0}, {"prompt": "<p>The exact value of $\\tan\\Large($$\\var{distheta}\\Large)$&nbsp;is</p>", "maxMarks": 0, "choices": ["<p>$\\dfrac{1}{2}$</p>", "<p>$\\dfrac{1}{\\sqrt{2}}$</p>", "<p>$\\dfrac{\\sqrt{3}}{2}$</p>", "<p>$\\dfrac{1}{\\sqrt{3}}$</p>", "<p>$\\sqrt{3}$</p>", "<p>$1$</p>"], "displayType": "radiogroup", "displayColumns": 0, "distractors": ["", "", "", "", "", ""], "variableReplacementStrategy": "originalfirst", "minMarks": 0, "shuffleChoices": true, "variableReplacements": [], "type": "1_n_2", "matrix": ["0", "0", "0", "if(theta=30,1,0)", "if(theta=60,1,0)", "if(theta=45,1,0)"], "scripts": {}, "showCorrectAnswer": true, "marks": 0}], "name": "Exact values for sin, cos, tan (acute, radians)", "tags": [], "ungrouped_variables": ["theta", "distheta"], "variables": {"distheta": {"definition": "if(theta=30,'\\$\\\\dfrac{\\\\pi}{6}\\$',if(theta=45,'\\$\\\\dfrac{\\\\pi}{4}\\$','\\$\\\\dfrac{\\\\pi}{3}\\$'))", "description": "<p>'\\$\\\\frac{\\pi}{6}\\$'</p>", "group": "Ungrouped variables", "name": "distheta", "templateType": "anything"}, "theta": {"definition": "random(30,45,60)", "description": "", "group": "Ungrouped variables", "name": "theta", "templateType": "anything"}}, "metadata": {"description": "<p>multiple choice testing sin, cos, tan&nbsp;of &nbsp;random(pi/6, pi/4, pi/3)&nbsp;radians</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "extensions": [], "variable_groups": [], "statement": "<p>Often we prefer to work with&nbsp;exact values rather than approximations from a calculator.</p>", "advice": "<p>By drawing the following triangles we can determine the exact values of $\\sin$, $\\cos$ and $\\tan$ (and their reciprocals $\\csc$, $\\sec$, $\\cot$) for the angles $\\dfrac{\\pi}{6}$, $\\dfrac{\\pi}{4}$&nbsp;and $\\dfrac{\\pi}{3}$.</p>\n<p><br/><br/><img src=\"resources/question-resources/exact_values_radians_We6EFEi.svg\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>Alternatively, one can memorise the following table:&nbsp;</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">$\\dfrac{\\pi}{6}$</td>\n<td style=\"text-align: center;\">$\\dfrac{\\pi}{4}$</td>\n<td style=\"text-align: center;\">$\\dfrac{\\pi}{3}$</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\sin$</td>\n<td style=\"text-align: center;\">$\\dfrac{1}{2}$</td>\n<td style=\"text-align: center;\">$\\dfrac{1}{\\sqrt{2}}$</td>\n<td style=\"text-align: center;\">$\\dfrac{\\sqrt{3}}{2}$</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\cos$</td>\n<td style=\"text-align: center;\">$\\dfrac{\\sqrt{3}}{2}$</td>\n<td style=\"text-align: center;\">$\\dfrac{1}{\\sqrt{2}}$</td>\n<td style=\"text-align: center;\">$\\dfrac{1}{2}$</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\tan$</td>\n<td style=\"text-align: center;\">$\\dfrac{1}{\\sqrt{3}}$</td>\n<td style=\"text-align: center;\">$1$</td>\n<td style=\"text-align: center;\">$\\sqrt{3}$</td>\n</tr>\n</tbody>\n</table>", "functions": {}, "question_groups": [{"questions": [], "pickingStrategy": "all-ordered", "name": "", "pickQuestions": 0}], "rulesets": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}