// Numbas version: exam_results_page_options {"name": "Exact values for sin, cos, tan (acute, degrees)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/exact_values.svg", "/srv/numbas/media/question-resources/exact_values.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"type": "question", "variablesTest": {"condition": "", "maxRuns": 100}, "showQuestionGroupNames": false, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "

multiple choice testing sin, cos, tan of random(30, 45, 60) degrees

"}, "parts": [{"scripts": {}, "displayColumns": 0, "matrix": ["if(theta=30,1,0)", "if(theta=45,1,0)", "if(theta=60,1,0)", 0, 0, 0], "showCorrectAnswer": true, "prompt": "

The exact value of $\\sin(\\var{theta}^\\circ)$ is

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$\\dfrac{1}{2}$

", "

$\\dfrac{1}{\\sqrt{2}}$

", "

$\\dfrac{\\sqrt{3}}{2}$

", "

$\\dfrac{1}{\\sqrt{3}}$

", "

$\\sqrt{3}$

", "

$1$

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The exact value of $\\cos(\\var{theta}^\\circ)$ is

$\\dfrac{1}{2}$

", "

$\\dfrac{1}{\\sqrt{2}}$

", "

$\\dfrac{\\sqrt{3}}{2}$

", "

$\\dfrac{1}{\\sqrt{3}}$

", "

$\\sqrt{3}$

", "

$1$

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The exact value of $\\tan(\\var{theta}^\\circ)$ is

$\\dfrac{1}{2}$

", "

$\\dfrac{1}{\\sqrt{2}}$

", "

$\\dfrac{\\sqrt{3}}{2}$

", "

$\\dfrac{1}{\\sqrt{3}}$

", "

$\\sqrt{3}$

", "

$1$

"]}], "name": "Exact values for sin, cos, tan (acute, degrees)", "advice": "

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 $30^\\circ$, $45^\\circ$ and $60^\\circ$.

Alternatively, one can memorise the following table:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

	$30^\\circ$	$45^\\circ$	$60^\\circ$

$\\sin$	$\\dfrac{1}{2}$	$\\dfrac{1}{\\sqrt{2}}$	$\\dfrac{\\sqrt{3}}{2}$

$\\cos$	$\\dfrac{\\sqrt{3}}{2}$	$\\dfrac{1}{\\sqrt{2}}$	$\\dfrac{1}{2}$

$\\tan$	$\\dfrac{1}{\\sqrt{3}}$	$1$	$\\sqrt{3}$

", "preamble": {"js": "", "css": ""}, "functions": {}, "tags": ["exact values", "trigonometry"], "variable_groups": [], "ungrouped_variables": ["theta"], "statement": "

Often we prefer to work with exact values rather than approximations from a calculator.

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