Difference between revisions of "Arc"

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An '''arc''' of a [[circle]] is a segment of the circle.
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An '''arc''' of a [[circle]] is the portion of the circle between two given points on the circle.  More generally, an arc is a portion of a smooth curve joining two points.
  
The length of an arc can be calculated by the formula <math>s = r\theta</math>, where <math>r</math> is the [[radius]] and <math>\theta</math> is the [[central angle]] in degrees.
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The ''measure'' of a circular arc <math>AB</math> on circle <math>O</math> is defined to be the measure of the [[central angle]] <math>\angle AOB</math> which has the arc on its [[interior of an angle | interior]].  The length of an arc can be calculated by the formula <math>s = r\theta</math>, where <math>r</math> is the [[radius]] of the circle and <math>\theta</math> is the measure of the arc, in [[radian]]s.  Thus, in particular, the [[circumference]] of a circle is given by <math>C = 2\pi</math>.
  
 
== Problems ==
 
== Problems ==
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=== Olympiad ===
 
=== Olympiad ===
  
== See also ==
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== Alternate usage ==
*[[Inverse trigonometric function]]s
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Arc is also used as a prefix.  For each of the standard [[trigonometric function]]s, the arc-function is (one of) the corresponding [[inverse of a function | inverse function]].  For example, the [[arcsine]] is the inverse of the [[sine]].
  
 
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[[Category:Geometry]]
 
[[Category:Geometry]]

Revision as of 20:41, 4 March 2007

An arc of a circle is the portion of the circle between two given points on the circle. More generally, an arc is a portion of a smooth curve joining two points.

The measure of a circular arc $AB$ on circle $O$ is defined to be the measure of the central angle $\angle AOB$ which has the arc on its interior. The length of an arc can be calculated by the formula $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the measure of the arc, in radians. Thus, in particular, the circumference of a circle is given by $C = 2\pi$.

Problems

Introductory

Intermediate

Olympiad

Alternate usage

Arc is also used as a prefix. For each of the standard trigonometric functions, the arc-function is (one of) the corresponding inverse function. For example, the arcsine is the inverse of the sine.

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