1. Radian Measure Angles can be measured 3 ways: 1) Degrees (360 parts to a rotation) 1) Degrees (360 parts to a rotation) used for triangle applications used for triangle applications 2) Radians (2 ∏ parts to a rotation) 2) Radians (2 ∏ parts to a rotation) used for circular applications used for circular applications 3) Grads (100 parts to a rotation) 3) Grads (100 parts to a rotation) used by the military used by the military

2. Radian Measure Place an angle with the vertex at the center of a circle.

3. Radian Measure An angle measured in radians is the ratio of the arc length of the circle to the radius of the circle. radius θ

4. What is a radian? In science and engineering, radians are much more convenient (and common) than degrees. A radian is defined as the angle between 2 radii (radiuses) of a circle where the arc between them has length of one radius. Another way of putting it is: "a radian is the angle subtended by an arc of length r (the radius)". One radian is about 57.3°.

5. Radian Measure radius θ We will use the formula: where S is the arc length, r is the radius, and is the angle in radians

6. Find the length of the arc shown: (round to the nearest tenth) =30.6 ft

7. Find the central angle: (round to the nearest tenth) =2.4 radians

8. Radian Measure Conversion Factor: Sometimes it is necessary to convert radians to degrees and degrees to radians.

9. Radian Measure 30° can be converted to radians by…

10. Radian Measure can be converted to degrees by…

11. Whiteboards Ready?

12. Radian Measure 45°= _____________ radians Think…

13. Radian Measure 60°= _____________ radians Think…

14. Radian Measure 315°= _____________ radians Think…           180 315 

15. Radian Measure 120°= _____________ radians Think…           180 120 

16. Radian Measure radians= _______ degrees Think…

17. Radian Measure radians= _______ degrees Think…

18. Radian Measure radians= _______ degrees Think…

19. Radian Measure radians= _______ degrees Think…

20. How about this? Find the exact value of sin

21. Go to the Practice!!! What is ? Have fun. Have fun. Mwahaha….. Mwahaha…..