Difference between revisions of "Arc"
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| − | An '''arc''' of a [[circle]] is | + | 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 [[ | + | 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 === | ||
| − | == | + | == 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 of a function | inverse function]]. For example, the arcsine is the inverse of the [[sine]]. | |
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[[Category:Geometry]] | [[Category:Geometry]] | ||
Latest revision as of 23:24, 15 December 2023
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 
on circle 
is defined to be the measure of the central angle 
which has the arc on its interior. The length of an arc can be calculated by the formula 
, where 
is the radius of the circle and 
is the measure of the arc, in radians. Thus, in particular, the circumference of a circle is given by 
.
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.
