This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Section 4.2 – Radians, Arc Length, and the Area of a Sector 1 Section 4.2 Radians, Arc Length, and Area of a Sector An angle is formed by two rays that have a common endpoint ( vertex) . One ray is the initial side and the other is the terminal side . We typically will draw angles in the coordinate plane with the initial side along the positive x axis. A Terminal side θ Vertex B Initial Side C θ and , , , CBA ABC B ∠ ∠ ∠ are all notations for this angle. When using the notation , and CBA ABC ∠ ∠ the vertex is always the middle letter. We measure angles in two different ways, both of which rely on the idea of a complete revolution in a circle. The first is degree measure. In this system of angle measure one complete revolution is ° 360 . So one degree is 360 1 of the circle. The second method is called radian measure. One complete revolution is π 2 . The problems in this section are worked in radians. Radians is a unit free measurement. The Radian Measure of an Angle Place the vertex of the angle at the center of a circle of radius r . Let s denote the length of the arc intercepted by the angle. The radian measure θ of the angle is the ratio of the arc length s to the radius r . In symbols, r s = θ . In this definition it is assumed that s and r have the same linear units. s θ r One radian measure is the measure of the central angle (vertex of the angle is at the center of the circle) of a circle that intercepts an arc equal in length to the radius of the circle. circle) of a circle that intercepts an arc equal in length to the radius of the circle....
View
Full
Document
This note was uploaded on 02/20/2012 for the course MATH 1330 taught by Professor Staff during the Fall '08 term at University of Houston.
 Fall '08
 Staff
 Arc Length, Angles

Click to edit the document details