Radian: Difference between revisions
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A '''radian''' is the [[angle]] subtended by an [[arc length]] equal to the radius of a circle. There are 2[[pi|π]] radians in a full circle, as the arc length of the circumference of a circle is equal to 2π times the radius of the circle. | A '''radian''' is the [[angle]] subtended by an [[arc length]] equal to the radius of a circle. There are 2[[pi|π]] radians in a full circle, as the arc length of the circumference of a circle is equal to 2π times the radius of the circle. | ||
Measuring angles in radians often allows the direct use of angles in mathematical formulae, particularly in [[trigonometric function]]s and their expansions. | 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 | |||
==Other units== | ==Other units== | ||
Revision as of 22:54, 21 June 2007
A radian is the angle subtended by an arc length equal to the radius of a circle. There are 2π radians in a full circle, as the arc length of the circumference of a circle is equal to 2π 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 x is expressed in radians
Other units
- 1 radian is equal to 180/π or 57.295 779 513... degrees of arc
- 1 radian is equal to 200/π or 63.661 977 237... grads