{"id":33562,"date":"2025-06-23T09:26:30","date_gmt":"2025-06-23T09:26:30","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=33562"},"modified":"2025-06-23T09:26:33","modified_gmt":"2025-06-23T09:26:33","slug":"convert-the-following-angle-from-degrees-to-radians-2","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/convert-the-following-angle-from-degrees-to-radians-2\/","title":{"rendered":"Convert the following angle from degrees to radians."},"content":{"rendered":"\n

Convert the following angle from degrees to radians. Express your answer in simplest form. 555\u00c2\u00b0<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

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

To convert 555\u00b0<\/strong> to radians:<\/p>\n\n\n\n

We use the formula:Radians=Degrees\u00d7(\u03c0180)\\text{Radians} = \\text{Degrees} \\times \\left( \\frac{\\pi}{180} \\right)Radians=Degrees\u00d7(180\u03c0\u200b)<\/p>\n\n\n\n

Step 1:<\/strong> Multiply 555 by \u03c0 and divide by 180555\u2218\u00d7(\u03c0180)=555\u03c0180555^\\circ \\times \\left( \\frac{\\pi}{180} \\right) = \\frac{555\\pi}{180}555\u2218\u00d7(180\u03c0\u200b)=180555\u03c0\u200b<\/p>\n\n\n\n

Step 2:<\/strong> Simplify the fraction
First, find the greatest common divisor (GCD) of 555 and 180. Both numbers are divisible by 15.<\/p>\n\n\n\n

Divide numerator and denominator by 15:555\u00f715180\u00f715=37\u03c012\\frac{555 \\div 15}{180 \\div 15} = \\frac{37\\pi}{12}180\u00f715555\u00f715\u200b=1237\u03c0\u200b<\/p>\n\n\n\n

Final Answer:<\/strong>555\u2218=37\u03c012 radians555^\\circ = \\frac{37\\pi}{12} \\text{ radians}555\u2218=1237\u03c0\u200b radians<\/p>\n\n\n\n

\n\n\n\n

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

To convert an angle from degrees to radians, we use the standard conversion factor between these two units. One full revolution around a circle is 360 degrees, which is equal to 2\u03c02\\pi2\u03c0 radians. This means that:1\u2218=\u03c0180 radians1^\\circ = \\frac{\\pi}{180} \\text{ radians}1\u2218=180\u03c0\u200b radians<\/p>\n\n\n\n

This relationship allows us to convert any degree measure into radians by multiplying the degree measure by \u03c0180\\frac{\\pi}{180}180\u03c0\u200b.<\/p>\n\n\n\n

In this problem, the angle given is 555 degrees. To convert this to radians, we multiply:555\u2218\u00d7(\u03c0180)=555\u03c0180555^\\circ \\times \\left( \\frac{\\pi}{180} \\right) = \\frac{555\\pi}{180}555\u2218\u00d7(180\u03c0\u200b)=180555\u03c0\u200b<\/p>\n\n\n\n

Next, we simplify the fraction 555180\\frac{555}{180}180555\u200b. To do this, we find the greatest common divisor (GCD) of 555 and 180. Using prime factorization:<\/p>\n\n\n\n

    \n
  • 555 = 5 \u00d7 111 = 5 \u00d7 3 \u00d7 37<\/li>\n\n\n\n
  • 180 = 2 \u00d7 2 \u00d7 3 \u00d7 3 \u00d7 5<\/li>\n<\/ul>\n\n\n\n

    The common factors are 3 and 5, so the GCD is 15.<\/p>\n\n\n\n

    We divide both numerator and denominator by 15:555\u00f715180\u00f715=3712\\frac{555 \\div 15}{180 \\div 15} = \\frac{37}{12}180\u00f715555\u00f715\u200b=1237\u200b<\/p>\n\n\n\n

    So, the simplified form is:37\u03c012 radians\\frac{37\\pi}{12} \\text{ radians}1237\u03c0\u200b radians<\/p>\n\n\n\n

    This is the simplest exact form. The angle in radians provides a more natural way to describe angles in terms of the circle’s geometry, especially in trigonometry and calculus.<\/p>\n\n\n\n

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

    Convert the following angle from degrees to radians. Express your answer in simplest form. 555\u00c2\u00b0 The Correct Answer and Explanation is: Correct Answer: To convert 555\u00b0 to radians: We use the formula:Radians=Degrees\u00d7(\u03c0180)\\text{Radians} = \\text{Degrees} \\times \\left( \\frac{\\pi}{180} \\right)Radians=Degrees\u00d7(180\u03c0\u200b) Step 1: Multiply 555 by \u03c0 and divide by 180555\u2218\u00d7(\u03c0180)=555\u03c0180555^\\circ \\times \\left( \\frac{\\pi}{180} \\right) = \\frac{555\\pi}{180}555\u2218\u00d7(180\u03c0\u200b)=180555\u03c0\u200b Step […]<\/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-33562","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33562","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=33562"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33562\/revisions"}],"predecessor-version":[{"id":33568,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33562\/revisions\/33568"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=33562"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=33562"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=33562"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}