2. Radian Measure (3.1) JMerrill, 2007 Revised 2000

3. A Newer Kind of Angle Measurement: The Radian 11 radian = the measure of the central angle of a circle that intercepts an arc equal in length to the radius of the circle. r r r θ The central angle is an angle that has its vertex at the center of a circle

4. The Radian 1 radian ≈ 57.3 o 2 radians ≈ 114.6 o 3 radians ≈ 171.9 o 4 radians ≈ 229.2 o 5 radians ≈ 286.5 o 6 radians ≈ 343.8 o

5. Conversion Factor Between Radians and Degrees Radians can be expressed in decimal form or exact answers. The majority of the time, answers will be exact--left in terms of pi

6. You Do 1196 o = ? Radians (exact answer) 11.35 radians = ? degrees

7. Arc Length IIn geometry, an arc length is represented by “s”  If any of these parts are unknown, use the formula r r s θ Where theta is in radians

8. Arc Length EExample: A circle has a radius of 4 inches. Find the length of the arc intercepted by a central angle of 240 o. WWe will use s = rθ, but first we have to convert 240 o to radians.

9. Things You MUST Remember: ππ radians = 180 degrees ( ½ revolution) 22π radians = 360 degrees (1 revolution) ¼¼ revolution = ? degrees = ? radians  90 degrees π/2 radians

10. Exact Angle Measurement AAngle measures that can be expressed evenly in degrees cannot be expressed evenly in radians, and vice versa. So, we use fractional multiples of π.

11. Quadrant angles 0o0o 180 o π 360 o

12. Special Angles & The Unit Circle P130

13. Evaluating Trig Functions for Angles Using Radian Measure EEvaluate in exact terms  is equivalent to what degree? SSo 60 o

14. You Do EEvaluate in exact terms

15. Recall: Reference Angles Reference Angle: the smallest positive acute angle determined by the x-axis and the terminal side of θ ref angle

16. Find Reference Angle 150° 30° 225° 45° 300° 60°

17. Using Reference Angles a) sin 330° = = - sin 30° = - 1/2 b) cos 0° = = 1

18. Using Reference Angles