To convert an angle from degrees to radians, we use the following formula:radians=degrees\u00d7\u03c0180\\text{radians} = \\text{degrees} \\times \\frac{\\pi}{180}radians=degrees\u00d7180\u03c0\u200b<\/p>\n\n\n\n
Step 1: Apply the Formula<\/h3>\n\n\n\n
Given:\u2212390\u2218-390^\\circ\u2212390\u2218<\/p>\n\n\n\n
Using the formula:\u2212390\u2218\u00d7\u03c0180=\u2212390\u03c0180-390^\\circ \\times \\frac{\\pi}{180} = \\frac{-390\\pi}{180}\u2212390\u2218\u00d7180\u03c0\u200b=180\u2212390\u03c0\u200b<\/p>\n\n\n\n
Now simplify the fraction:\u2212390\u03c0180=\u221213\u03c06\\frac{-390\\pi}{180} = \\frac{-13\\pi}{6}180\u2212390\u03c0\u200b=6\u221213\u03c0\u200b<\/p>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
\u221213\u03c06 radians\\boxed{-\\frac{13\\pi}{6}} \\text{ radians}\u2212613\u03c0\u200b\u200b radians<\/p>\n\n\n\n
\n\n\n\n
Explanation<\/h3>\n\n\n\n
The process of converting degrees to radians involves a fundamental understanding of how angle measurement units relate. Degrees and radians are two different ways to measure angles, with degrees being more common in everyday use, and radians being more natural in advanced mathematics, especially in calculus and trigonometry.<\/p>\n\n\n\n
One complete circle measures 360 degrees<\/strong>, which is equal to 2\u03c02\\pi2\u03c0 radians<\/strong>. From this, we derive the conversion factor:1\u2218=\u03c0180 radians1^\\circ = \\frac{\\pi}{180} \\text{ radians}1\u2218=180\u03c0\u200b radians<\/p>\n\n\n\n So, to convert any angle in degrees to radians, we multiply it by \u03c0180\\frac{\\pi}{180}180\u03c0\u200b. In this case, we were asked to convert \u2212390\u2218-390^\\circ\u2212390\u2218<\/strong> into radians. Note that the angle is negative, which means it is measured in the clockwise direction. This does not change the conversion process\u2014just carry the negative sign throughout.<\/p>\n\n\n\n We start by plugging the value into the formula:\u2212390\u00d7\u03c0180=\u2212390\u03c0180-390 \\times \\frac{\\pi}{180} = \\frac{-390\\pi}{180}\u2212390\u00d7180\u03c0\u200b=180\u2212390\u03c0\u200b<\/p>\n\n\n\n We then simplify the fraction. Both 390 and 180 are divisible by 30:\u2212390\u03c0180=\u221213\u03c06\\frac{-390\\pi}{180} = \\frac{-13\\pi}{6}180\u2212390\u03c0\u200b=6\u221213\u03c0\u200b<\/p>\n\n\n\n This result is in terms of \u03c0\\pi\u03c0, which keeps the value exact. This is important in mathematics because it avoids approximation errors that come from using decimal representations of \u03c0\\pi\u03c0.<\/p>\n\n\n\n Understanding this result is also helpful in trigonometry. For instance, \u221213\u03c06-\\frac{13\\pi}{6}\u2212613\u03c0\u200b radians is equivalent to rotating clockwise past two full circles (since 2\u03c0=12\\pi = 12\u03c0=1 full circle), then an additional \u2212\u03c06-\\frac{\\pi}{6}\u22126\u03c0\u200b. That\u2019s useful for interpreting angles on the unit circle.<\/p>\n\n\n\n Thus, the exact radian measure of \u2212390\u2218-390^\\circ\u2212390\u2218<\/strong> is:\u221213\u03c06\\boxed{-\\frac{13\\pi}{6}}\u2212613\u03c0\u200b\u200b<\/p>\n\n\n\n Convert -390 degree to radian measure. Write your answer as an exact value. The Correct Answer and Explanation is: To convert an angle from degrees to radians, we use the following formula:radians=degrees\u00d7\u03c0180\\text{radians} = \\text{degrees} \\times \\frac{\\pi}{180}radians=degrees\u00d7180\u03c0\u200b Step 1: Apply the Formula Given:\u2212390\u2218-390^\\circ\u2212390\u2218 Using the formula:\u2212390\u2218\u00d7\u03c0180=\u2212390\u03c0180-390^\\circ \\times \\frac{\\pi}{180} = \\frac{-390\\pi}{180}\u2212390\u2218\u00d7180\u03c0\u200b=180\u2212390\u03c0\u200b Now simplify the fraction:\u2212390\u03c0180=\u221213\u03c06\\frac{-390\\pi}{180} = \\frac{-13\\pi}{6}180\u2212390\u03c0\u200b=6\u221213\u03c0\u200b […]<\/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 center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-230873","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230873","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=230873"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230873\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=230873"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=230873"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=230873"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-810.jpeg\")
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