{"id":230963,"date":"2025-06-10T09:13:40","date_gmt":"2025-06-10T09:13:40","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=230963"},"modified":"2025-06-10T09:13:42","modified_gmt":"2025-06-10T09:13:42","slug":"convert-the-angle-measure-from-radians-to-degrees-5pi-12-is-the-same-as-what","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/10\/convert-the-angle-measure-from-radians-to-degrees-5pi-12-is-the-same-as-what\/","title":{"rendered":"Convert the angle measure from radians to degrees. -5pi\/12 is the same as what"},"content":{"rendered":"\n

Convert the angle measure from radians to degrees. -5pi\/12 is the same as what<\/p>\n\n\n\n

To convert \u22125\u03c012-\\frac{5\\pi}{12}\u2212125\u03c0\u200b radians to degrees, use the conversion factor:1 radian=180\u2218\u03c01 \\text{ radian} = \\frac{180^\\circ}{\\pi}1 radian=\u03c0180\u2218\u200b<\/p>\n\n\n\n

Step-by-step Conversion:<\/h3>\n\n\n\n

\u22125\u03c012 radians=\u22125\u03c012\u00d7180\u2218\u03c0-\\frac{5\\pi}{12} \\text{ radians} = -\\frac{5\\pi}{12} \\times \\frac{180^\\circ}{\\pi}\u2212125\u03c0\u200b radians=\u2212125\u03c0\u200b\u00d7\u03c0180\u2218\u200b<\/p>\n\n\n\n

Cancel out \u03c0\\pi\u03c0:=\u22125\u00d7180\u221812= -\\frac{5 \\times 180^\\circ}{12}=\u2212125\u00d7180\u2218\u200b=\u2212900\u221812= -\\frac{900^\\circ}{12}=\u221212900\u2218\u200b=\u221275\u2218= -75^\\circ=\u221275\u2218<\/p>\n\n\n\n

Final Answer:<\/h3>\n\n\n\n

\u22125\u03c012 radians=\u221275\u2218-\\frac{5\\pi}{12} \\text{ radians} = -75^\\circ\u2212125\u03c0\u200b radians=\u221275\u2218<\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/h3>\n\n\n\n

Angles can be measured in radians<\/strong> or degrees<\/strong>, which are two different units for the same concept. Radians are often used in mathematics and physics, especially when dealing with trigonometric functions and calculus. Degrees, on the other hand, are more commonly used in geometry and everyday applications.<\/p>\n\n\n\n

To convert an angle from radians to degrees, we use the fact that a full circle is 2\u03c02\\pi2\u03c0 radians or 360\u2218360^\\circ360\u2218. From this relationship, we derive the conversion factor:1 radian=180\u2218\u03c01 \\text{ radian} = \\frac{180^\\circ}{\\pi}1 radian=\u03c0180\u2218\u200b<\/p>\n\n\n\n

This tells us that to convert any radian measure to degrees, we multiply it by 180\u2218\u03c0\\frac{180^\\circ}{\\pi}\u03c0180\u2218\u200b.<\/p>\n\n\n\n

In the case of \u22125\u03c012-\\frac{5\\pi}{12}\u2212125\u03c0\u200b, we start by multiplying it by 180\u2218\u03c0\\frac{180^\\circ}{\\pi}\u03c0180\u2218\u200b. The \u03c0\\pi\u03c0 terms cancel out, and we are left with:\u22125\u00d718012-\\frac{5 \\times 180}{12}\u2212125\u00d7180\u200b<\/p>\n\n\n\n

We then calculate the numerator: 5\u00d7180=9005 \\times 180 = 9005\u00d7180=900, and divide by 12, which gives us 75. Because the original angle was negative, the final answer is \u221275\u2218-75^\\circ\u221275\u2218.<\/p>\n\n\n\n

A negative angle means the rotation is clockwise<\/strong>, as opposed to a positive angle, which represents a counterclockwise<\/strong> rotation. So, \u22125\u03c012-\\frac{5\\pi}{12}\u2212125\u03c0\u200b radians is a clockwise rotation of 75 degrees from the positive x-axis.<\/p>\n\n\n\n

Understanding this conversion is fundamental in trigonometry, engineering, physics, and computer graphics where angle measures often need to be translated between the two units depending on the context.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

Convert the angle measure from radians to degrees. -5pi\/12 is the same as what To convert \u22125\u03c012-\\frac{5\\pi}{12}\u2212125\u03c0\u200b radians to degrees, use the conversion factor:1 radian=180\u2218\u03c01 \\text{ radian} = \\frac{180^\\circ}{\\pi}1 radian=\u03c0180\u2218\u200b Step-by-step Conversion: \u22125\u03c012 radians=\u22125\u03c012\u00d7180\u2218\u03c0-\\frac{5\\pi}{12} \\text{ radians} = -\\frac{5\\pi}{12} \\times \\frac{180^\\circ}{\\pi}\u2212125\u03c0\u200b radians=\u2212125\u03c0\u200b\u00d7\u03c0180\u2218\u200b Cancel out \u03c0\\pi\u03c0:=\u22125\u00d7180\u221812= -\\frac{5 \\times 180^\\circ}{12}=\u2212125\u00d7180\u2218\u200b=\u2212900\u221812= -\\frac{900^\\circ}{12}=\u221212900\u2218\u200b=\u221275\u2218= -75^\\circ=\u221275\u2218 Final Answer: \u22125\u03c012 radians=\u221275\u2218-\\frac{5\\pi}{12} \\text{ radians} = -75^\\circ\u2212125\u03c0\u200b radians=\u221275\u2218 Explanation: Angles can […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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