Difference between revisions of "Radian"

 
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A '''radian''' is a unit of measurement for [[angle|angles]]. In a circle, the measure of a [[central angle]] in radians is the ratio of the length of the [[intercepted arc]] to the length of the circle's [[radius]].
 
A '''radian''' is a unit of measurement for [[angle|angles]]. In a circle, the measure of a [[central angle]] in radians is the ratio of the length of the [[intercepted arc]] to the length of the circle's [[radius]].
  
A complete angle has measure <math>2\pi</math>, since a complete angle "intercepts" the whole circumference of the circle. Thus, radians can be converted to [[Degree (geometry)|degrees]]: <math>2\pi\; rad=360^\circ</math> or <math>\pi \;rad=180^\circ</math>.
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In a unitcircle, a complete angle has measure <math>2\pi</math>, since a complete angle "intercepts" the whole circumference of the circle. Thus, radians can be converted to [[Degree (geometry)|degrees]]: <math>2\pi\; rad=360^\circ\implies\pi \;rad=180^\circ</math>.
  
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[[Category:Geometry]]
 
[[Category:Geometry]]
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[[Category:Definition]]

Latest revision as of 18:30, 10 March 2014

A radian is a unit of measurement for angles. In a circle, the measure of a central angle in radians is the ratio of the length of the intercepted arc to the length of the circle's radius.

In a unitcircle, a complete angle has measure $2\pi$, since a complete angle "intercepts" the whole circumference of the circle. Thus, radians can be converted to degrees: $2\pi\; rad=360^\circ\implies\pi \;rad=180^\circ$.

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