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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 Vertex B Initial Side C 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 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 of the angle is the ratio of the arc length s to the radius r . In symbols, r s = . In this definition it is assumed that s and r have the same linear units. s 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....
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