convert 50 degrees to radians (exact answers only)<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n To convert degrees to radians, the formula is: radians=degrees\u00d7\u03c0180\\text{radians} = \\text{degrees} \\times \\frac{\\pi}{180}<\/p>\n\n\n\n Given 50 degrees, substitute it into the formula: 50\u2218\u00d7\u03c0180=50\u03c018050^\\circ \\times \\frac{\\pi}{180} = \\frac{50\\pi}{180}<\/p>\n\n\n\n Simplify the fraction by dividing numerator and denominator by 10: 50\u03c0180=5\u03c018\\frac{50\\pi}{180} = \\frac{5\\pi}{18}<\/p>\n\n\n\n Therefore, 50 degrees in radians is: 5\u03c018\\boxed{\\frac{5\\pi}{18}}<\/p>\n\n\n\n Explanation<\/strong><\/p>\n\n\n\n Radians and degrees are two units used to measure angles. Degrees divide one full rotation into 360 equal parts, while radians divide the same rotation based on the radius of a circle. One full circle is 360\u2218360^\\circ or 2\u03c02\\pi radians.<\/p>\n\n\n\n Since 360\u2218=2\u03c0360^\\circ = 2\\pi radians, it follows that: 1\u2218=2\u03c0360=\u03c0180 radians1^\\circ = \\frac{2\\pi}{360} = \\frac{\\pi}{180} \\text{ radians}<\/p>\n\n\n\n This relationship allows converting any angle from degrees to radians by multiplying the degree value by \u03c0180\\frac{\\pi}{180}.<\/p>\n\n\n\n The answer remains in terms of \u03c0\\pi for an exact representation, since \u03c0\\pi is an irrational number. Decimal approximations lose precision and are not exact.<\/p>\n\n\n\n Simplifying the fraction reduces the result to its simplest form, making it easier to understand or use in further calculations.<\/p>\n\n\n\n In summary, converting degrees to radians involves multiplying by \u03c0180\\frac{\\pi}{180}, and simplifying fractions leads to exact and neat answers such as 5\u03c018\\frac{5\\pi}{18} for 50 degrees.<\/p>\n","protected":false},"excerpt":{"rendered":" convert 50 degrees to radians (exact answers only) The correct answer and explanation is: To convert degrees to radians, the formula is: radians=degrees\u00d7\u03c0180\\text{radians} = \\text{degrees} \\times \\frac{\\pi}{180} Given 50 degrees, substitute it into the formula: 50\u2218\u00d7\u03c0180=50\u03c018050^\\circ \\times \\frac{\\pi}{180} = \\frac{50\\pi}{180} Simplify the fraction by dividing numerator and denominator by 10: 50\u03c0180=5\u03c018\\frac{50\\pi}{180} = \\frac{5\\pi}{18} Therefore, 50 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-38287","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38287","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=38287"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38287\/revisions"}],"predecessor-version":[{"id":38288,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38287\/revisions\/38288"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=38287"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=38287"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=38287"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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