// Numbas version: exam_results_page_options {"name": "Converting angles from radians to degrees", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "functions": {}, "tags": [], "ungrouped_variables": ["d", "ans1", "m", "ans2", "a", "b", "ans3"], "statement": "

Please convert the following angles from radians to degrees.

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Convert from radians to degrees

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$\\displaystyle\\simplify{{m}*pi}=$ [[0]]$^\\circ$

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$\\displaystyle\\simplify{pi/{d}}=$ [[0]]$^\\circ$

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$\\displaystyle\\simplify{{a}*pi/{b}}=$ [[0]]$^\\circ$

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$\\pi$ radians is equal to $180^\\circ$. This means each $\\pi$ we see we can replace it with $180^\\circ$. In other words, to convert from radians to degrees we divide by $\\pi$ and multiply by $180^\\circ$.

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For example, $\\displaystyle \\frac{2\\pi}{5}=\\frac{2\\pi\\times 180^\\circ}{5\\pi}=\\frac{2\\times 180^\\circ}{5}=72^\\circ$.

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It is useful to memorise some of the very common angles, for example, $\\displaystyle \\frac{\\pi}{6}=30^\\circ,\\, \\frac{\\pi}{4}=45^\\circ,\\, \\frac{\\pi}{3}=60^\\circ, \\,\\frac{\\pi}{2}=90^\\circ, \\,\\pi=180^\\circ$ and $2\\pi=360^\\circ$.

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