Radian: Difference between revisions
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imported>Anthony Argyriou (add more) |
imported>Andrey Khalyavin (+math) |
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A '''radian''' is the [[angle]] subtended by an [[arc length]] equal to the radius of a circle. There are 2 | A '''radian''' is the [[angle]] subtended by an [[arc length]] equal to the radius of a circle. There are <math>2\pi</math> radians in a full circle, as the arc length of the circumference of a circle is equal to <math>2\pi</math> times the radius of the circle. | ||
The radian is considered a dimensionless derived unit in the [[International System of Units]]. | The radian is considered a dimensionless derived unit in the [[International System of Units]]. | ||
Measuring angles in radians often allows the direct use of angles in mathematical formulae, particularly in [[trigonometric function]]s and their expansions. The identity <math>\scriptstyle sin x = - sin'' x</math> is only true when x is expressed in radians | Measuring angles in radians often allows the direct use of angles in mathematical formulae, particularly in [[trigonometric function]]s and their expansions. The identity <math>\scriptstyle \sin x = - \sin'' x</math> is only true when <math>x</math> is expressed in radians | ||
==Other units== | ==Other units== | ||
*1 radian is equal to 180/ | *1 radian is equal to <math>180/\pi</math> or 57.295 779 513... [[degree (angular measure)|degrees of arc]] | ||
*1 radian is equal to 200/ | *1 radian is equal to <math>200/\pi</math> or 63.661 977 237... [[grad (angular measure)|grads]] | ||
==Trigonometric functions== | ==Trigonometric functions== | ||
Revision as of 22:44, 1 July 2007
A radian is the angle subtended by an arc length equal to the radius of a circle. There are radians in a full circle, as the arc length of the circumference of a circle is equal to times the radius of the circle.
The radian is considered a dimensionless derived unit in the International System of Units.
Measuring angles in radians often allows the direct use of angles in mathematical formulae, particularly in trigonometric functions and their expansions. The identity is only true when is expressed in radians
Other units
- 1 radian is equal to or 57.295 779 513... degrees of arc
- 1 radian is equal to or 63.661 977 237... grads
