1. 1-10-19 T1.1c Define Radians &Convert Between Radians and Degrees

2. OPENER: Simplify Simplify Convert to DMS 4. 274.4782° Convert to decimal degrees 198.464°

3. Change 2.67 days to days, hours, minutes, seconds: 2 16 4 48 We want to go from days to hours: = 16.08 hrs We want to go from hours to minutes: = 4.8 min We want to go from minutes to seconds: = 48 sec

4. Active Learning Assignment Questions?

5. LESSON: Radian Demonstration on the Elmo. Definition: Radian: the central angle of a circle that is created when the arc intercepted by the angle is equal in length to the radius of a circle. RADIANS HAVE NO UNITS. Radians can be expressed as π radians or decimal radians. For example: or for example 2.09 (Notice, no symbol or unit, degree or otherwise).

6. II I III IV What would the π radian measure be at the quadrangle angles? In which quadrant is: → I → II 0 → IV → III

7. II I III IV What would the decimal radian measure be at the quadrangle angles? = 1.57 In which quadrant is: 1) 2 radians? → II 2) 3.5 radians? → III 0 = 3.14 = 6.28 3) 7 radians? → I 4) –1.2 radians? → IV = 4.71

8. To convert from degrees to π radians. (180° = π) (π radians are ALWAYS a ratio, proper or improper.) GCF? 90° GCF? 30° 5 5 1) 450 ° 2) 150° 2 6 GCF? 15° –5 3) –75° 12

9. II. To convert from π radians to degrees. (180° = π)

10. To convert from degrees to decimal radians. • (180° = π) (Two decimal places) 1) 53° 2) -259° -4.52 (Use the 3.14 for this chapter ONLY!) (In the future chapters, you will use the π button!) 0.92

11. IV. To convert from decimal radians to degrees. (180° = π) (One decimal place.) 2) -4.17 1) 2.39 -239.0° 137.0°

12. Active Learning Assignment: P 261: 1-8, 11, 12, 13 Columns a & b only Note: we always do the WRITTEN EXERCISES, unless otherwise noted Words of Wisdom (WOW): “Return borrowed items in the same or better condition than when you got it and return it promptly!”