1. T1.1c Define Radians & Convert Between Radians and Degrees
T1.1c Define Radians & Convert Between Radians and Degrees

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

3. Change 2.67 days to days, hours, minutes, seconds:16 4 48
We want to go from days to hours:
= 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. What would the π radian measure be at the quadrangle angles?IV
III II
In which quadrant is:
→ I
→ II
→ IV
→ III

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

8. To convert from degrees to π radians
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) °
2) 150° 2
GCF?
15° 6
– 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) 1)
-239.0°
137.0°

12. Note: we always do the WRITTEN EXERCISES, unless otherwise noted
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!”