1. Angles and Their Measure
Chapter 6.1

2. Angles are formed by two rays that have a common endpoint (vertex).
The first ray you draw is called the initial side.
The second ray you draw is called the terminal side.

3. We can use a coordinate system with angles by putting the initial side along the positive x-axis with the vertex at the origin. This is called being in standard position.
Rotation Matters!!!!
Terminal Side
This is a counterclockwise rotation.
This is a clockwise rotation.
Initial Side

4. Positive and negative angles depend on the ROTATION!!!
Terminal Side
45°
Initial Side
Positive angles are drawn in a counter-clockwise rotation.
Initial Side
- 45°
Terminal Side
Negative angles are drawn in a clockwise rotation.

5. Let’s look at some popular angles.
Angles on the axes are called quadrantal angles.
90°
180°
360°
270°

6. Draw an angle with the given measure in standard position.
50°
90°
180°
360°
270°

7. Draw an angle with the given measure in standard position.
135°
90°
180°
360°
270°

8. Draw an angle with the given measure in standard position.
240°
90°
180°
360°
270°

9. Draw an angle with the given measure in standard position.
330°
90°
180°
360°
270°

10. Draw an angle with the given measure in standard position.
-165°
90°
180°
360°
270°

11. Draw an angle with the given measure in standard position.
-315°
90°
180°
360°
270°

12. Going beyond 360 degrees.
440°
-360°
80°
90°
180°
360°
270°

13. Going beyond 360 degrees.
710°
-360°
350°
90°
180°
360°
270°

14. Going beyond 360 degrees. 825° -360° 465° -360° 105° 90° 180° 360°
270°

15. Name a possible value for the angle.
45°
-675°
-45°
-315°
405°
225°
90°
45°
180°
360°
Coterminal Angles
270°

16. State if the given angles are coterminal.NO
YES
YES

17. Find a positive and a negative coterminal angle for each given angle.

18. Radian Measure s Θ = r A second way to measure angles is in radians.
A radian is the ratio between the length of the arc and its radius. s
Θ = r

19. The Radian s Θ = r 1 radian ≈ 57.3o 2 radians ≈ 114.6o

20. Radian Measure

21. Quadrantal angles
90o π
180o 0o
360o
270o

22. Conversions Between Degrees and Radians
To convert degrees to radians, multiply degrees by
° ° °

23. Conversions Between Degrees and Radians
To convert radians to degrees, multiply degrees by
1. π π π

24. MAKE SURE YOUR CALCULATOR IS IN THE RIGHT MODE!!!
Using a calculator, find the approximate value of each.
1. Cos π/5
.81 1
csc  =
sin θ
2. Csc 2π/3
1.15 1
sec  =
cos θ
3. Cot 7π/3
.58 1
cot  =
tan θ
4. Sec 7π/8
-1.08
MAKE SURE YOUR CALCULATOR IS IN THE RIGHT MODE!!!