Prentice Hall Algebra 2

13-3 Radian Measure

Objectives

To use radian measure for angles

To find the length of an arc of a circle

A solve it problem.
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A central angle of a circle is an angle with a vertex at the center of a circle. An intercepted arc is the portion of the circle with endpoints on the sides of the central angle and remaining points within the interior of the angle.

A central angle has a vertex at the center of a circle. The angle intercepts the circle in two places. The region of the circle between the initial and terminal sides of the angle, the arc, is labeled the intercepted arc.

A radian is the measure of a central angle that intercepts an arc with length equal to the radius of the circle. Radians, like degrees, measure the amount of rotation from the initial side to the terminal side of an angle.

A central angle has an intersected arc equaling the same length as the radius of the circle, equaling 1 radian.

Essential Understanding An angle with a full circle rotation measures 2π radians. An angle with a semicircle rotation measures π radians.


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Table of Contents

Prentice Hall Algebra 2 Chapter 1 Expressions, Equations, and Inequalities Chapter 2 Functions, Equations, and Graphs Chapter 3 Linear Systems Chapter 4 Quadratic Functions and Equations Chapter 5 Polynomials and Polynomial Functions Chapter 6 Radical Functions and Rational Exponents Chapter 7 Exponential and Logarithmic Functions Chapter 8 Rational Functions Chapter 9 Sequences and Series Chapter 10 Quadratic Relations and Conic Sections Chapter 11 Probability and Statistics Chapter 12 Matrices Chapter 13 Periodic Functions and Trigonometry Chapter 14 Trigonometric Identities and Equations Skills Handbook English/Spanish Illustrated Glossary Selected Answers Index Acknowledgments