AoPSWiki
Want to learn how to tackle those tough MATHCOUNTS and AMC counting and probability problems? Check out Art of Problem Solving's Introduction to Counting & Probability by David Patrick.

Arc

From AoPSWiki

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.

Contents

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.

Stay informed about new Art of Problem Solving developments.
Click here to join our mailing lists.
© Copyright 2008 AoPS Incorporated. All Rights Reserved. • FoundationPrivacyContact Us