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Unformatted text preview: Section 4.1 Angles and Radian Measure ANGLES A ray is a part of a line that has only one endpoint and extends forever if the opposite direction. An angle is formed by two rays that have a common endpoint. One ray is called the initial side (where the measurement of an angle starts) and the other ray is called the terminal side (where the measurement of an angle stops). The common endpoint of an angles initial side and terminal side is the vertex of the angle. Standard position-Angles vertex is at the origin of the rectangular coordinate system.-Angles initial side lies along the positive x-axis. Positive angles generated by counterclockwise rotation. Negative angles generated by clockwise rotation. When an angle is in standard position, its terminal side can lie in a quadrant. We say the angle lies in that quadrant . An angle is a quadrantal angle if its terminal side lies on the x-axis or on the y- axis. Degrees Angles are measured by determining the amount of rotation from the initial side to the terminal side. Degrees , symbolized by , is one type of measurement of angles. A complete rotation (circle) is 360. An acute angle , measures less than 90. A right angle measures 90 and is one quarter of a complete rotation. An obtuse angle measures more than 90, but less than 180. A straight angle measure 180 and is one-half a complete rotation. Radians Radians is another type of measurement of angles. We use a circle of radius, r , to measure an angle in radians. A central angle is an angle whose vertex is at the center of the circle. One radian is the measure of the central angle of a circle that intercepts an arc equal in length to the radius of the circle. The radian measure of any central angle is the length of the intercepted arc divided by the circles radius. Radian Measure Consider an arc of length s on a circle of radius r . The measure of the central angle, , that intercepts the arc is radians r s = . EX 1: Find the radian measure of the central angle of a circle with radius r that intercepts an arc of length s ....
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- Fall '08