{"id":5753,"date":"2013-04-23T13:46:19","date_gmt":"2013-04-23T13:46:19","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=5753"},"modified":"2014-12-02T08:27:03","modified_gmt":"2014-12-02T08:27:03","slug":"radian-measure","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2013\/04\/23\/radian-measure\/","title":{"rendered":"Radian Measure"},"content":{"rendered":"

Overview:\u00a0 What Is Radian Measure?<\/strong><\/p>\n

The radian measure is another unit of angle measurement.\u00a0 An angle has the measurement of one radian if the length of the arc it intercepts is equal to the measurement of one radius. The radian measurement has many applications in mathematics and physics, where the more familiar measurement of angles by degrees is not as useful.<\/p>\n

How Many Radians Are There in a Circle?<\/strong><\/p>\n

Suppose a circle has a radius of 3 units, and an arc is drawn that intercepts 6 units on the circumference.\u00a0 The number of radians is 6\/3 or 2.\u00a0 If the arc was all the way around the circumference of the circle (C), then the arc would be equal to C.\u00a0 Remembering how the measurement of the length of the circumference of the circle is derived as C=2\u03c0r, the number of radians will equal 2\u03c0r\/r or 2\u03c0.<\/p>\n

Converting Degrees to Radians and Radians to Degrees<\/strong><\/p>\n

If 2\u03c0 radians =360o<\/sup>, then \u03c0 radians =180o<\/sup>, by dividing both sides of the equation by 2.\u00a0 Therefore 1 radian will equal 180o<\/sup>\/\u03c0, or about 57.2958 degrees, and 1 degree will equal \u03c0\/180, or about 0.0175 radians.\u00a0 The angle in degrees will equal the angle in radians times 57.2958.\u00a0 The angle in radians will equal the angle in degrees times 0.0175.<\/p>\n

Relationship of Radian Measure to Trigonometric Functions<\/strong><\/p>\n

There are many uses of sine, cosine, and tangent in mathematics beyond the measurement of angles.\u00a0\u00a0 \u00a0Formulas used in math analysis and calculus measure angles in radians rather than degrees.\u00a0 They are based upon functions that are simplified into radians.\u00a0 For example, the relationships between exponential functions and sine and cosine functions are expressed in radian units rather than degrees.<\/p>\n

Applications of Radian Measure<\/strong><\/p>\n

Many measurements in physics, such as the phase difference between waves, are measured in radians.\u00a0 Military applications of targeting, as well as telescopic sights, \u00a0use thousandths of radians, because it is more convenient.\u00a0 The measurement of small angles in astronomy is also often done in decimal fractions of radians.<\/p>\n

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Overview:\u00a0 What Is Radian Measure? The radian measure is another unit of angle measurement.\u00a0 An angle has the measurement of one radian if the length of the arc it intercepts is equal to the measurement of one radius. The radian measurement has many applications in mathematics and physics, where the more familiar measurement of angles […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[14,18],"tags":[472,1472,1475],"class_list":["post-5753","post","type-post","status-publish","format-standard","hentry","category-pre-calculus","category-trigonometry","tag-degrees-to-radians","tag-radian-measure","tag-radians-to-degrees"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5753","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=5753"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5753\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=5753"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=5753"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=5753"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}