Measuring Angles in Radians

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Presentation transcript:

Measuring Angles in Radians 12-3-EXT Lesson Presentation Holt McDougal Geometry Holt Geometry

Objectives Use proportions to convert angle measures from degrees to radians.

Vocabulary radian

One unit of measurement for angles is degrees, which are based on a fraction of a circle. Another unit is called a radian, which is based on the relationship of the radius and arc length of a central angle in a circle.

If a central angle θ in a circle of radius r intercepts an arc of length r, the measure of θ is defined as 1 radian. Since the circumference of a circle of radius r is 2πr, an angle representing one complete rotation measures 2π radians, or 360°. 2π radians = 360° and π radians = 180° 1° = π radians 180° and 1 radian = Use these facts to convert between radians and degrees.

Example 1: Converting Degrees to Radians Convert each measure from degrees to radians. A. 85° 17 85° π radians 180° 36 = 17 π 36 A. 90° 1 90° π radians 180° 2 = π 2

Example 2: Converting Radians to Degrees Convert each measure from radians to degrees. 2π 3 A. 2 π 1 3 radians 60 180° Π radians = 120° π 6 B. π 1 6 radians 30 180° Π radians = 30°