1. Reference Angles & Unit Circle
Section 4.2
Precalculus PreAP/Dual, Revised ©2017
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§4.2: Reference Angles and Unit Circle

2. §4.2: Reference Angles and Unit Circle
Reference angle is a positive acute angle formed by the terminal side of ө and the 𝒙-axis. They are viewed as linear pairs. (Think: REFER’s back to the 𝒙-axis)
The main angle should be within 0 and 360 degrees.
No reference trigonometric values of measure are greater than 𝟗𝟎° or less than to 𝟎°
Quadrant I: 𝜽
Quadrant II: 𝟏𝟖𝟎°−𝜽
Quadrant III: 𝜽−𝟏𝟖𝟎°
Quadrant IV: 𝟑𝟔𝟎°−𝛉
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§4.2: Reference Angles and Unit Circle

3. Reference Angle Quadrants
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§4.2: Reference Angles and Unit Circle

4. §4.2: Reference Angles and Unit Circle
Example 1
Determine the reference angle for 𝜽=𝟏𝟑𝟓°
135°
45°
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§4.2: Reference Angles and Unit Circle

5. §4.2: Reference Angles and Unit Circle
Example 2
Determine the reference angle for 𝛉=− 𝟏𝟏𝝅 𝟔
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§4.2: Reference Angles and Unit Circle

6. §4.2: Reference Angles and Unit Circle
Example 3
Determine the reference angle for 𝜽=𝟑 𝑹𝒂𝒅𝒊𝒂𝒏𝒔
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§4.2: Reference Angles and Unit Circle

7. §4.2: Reference Angles and Unit Circle
Your Turn
Determine the reference angle for 𝛉=− 𝝅 𝟕
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§4.2: Reference Angles and Unit Circle

8. Degrees in the Unit Circle – 45°, 45°, 90°II
III IV
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§4.2: Reference Angles and Unit Circle

9. §4.2: Reference Angles and Unit Circle
Conversions
Convert 𝟒𝟓° to Radian Mode
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§4.2: Reference Angles and Unit Circle

10. Radians in the Unit Circle – 45°, 45°, 90°II
III IV
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§4.2: Reference Angles and Unit Circle

11. §4.2: Reference Angles and Unit Circle
Right Triangles – 45°, 45°, 90°
triangles (Drawing not to scale) Radius = 1
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§4.2: Reference Angles and Unit Circle

12. §4.2: Reference Angles and Unit Circle
Reminder
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§4.2: Reference Angles and Unit Circle

13. Creating the Unit Circle – 45°, 45°, 90°
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§4.2: Reference Angles and Unit Circle

14. Degrees in the Unit Circle – 30°, 60°, 90°II
III IV
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§4.2: Reference Angles and Unit Circle

15. §4.2: Reference Angles and Unit Circle
Conversions
Convert 𝟑𝟎° to Radian Mode
11/10/ :27 AM
§4.2: Reference Angles and Unit Circle

16. Radians in the Unit Circle – 30°, 60°, 90°II
III IV
11/10/ :27 AM
§4.2: Reference Angles and Unit Circle

17. Creating the Unit Circle – 30°, 60°, 90°
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§4.2: Reference Angles and Unit Circle

18. Degrees in the Unit Circle – 30°, 60°, 90°II
III IV
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§4.2: Reference Angles and Unit Circle

19. §4.2: Reference Angles and Unit Circle
Conversions
Convert 𝟔𝟎° to Radian Mode
11/10/ :27 AM
§4.2: Reference Angles and Unit Circle

20. Creating the Unit Circle – 30°, 60°, 90°
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§4.2: Reference Angles and Unit Circle

21. Degrees in the Unit Circle – 30°, 60°, 90°II
III IV
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§4.2: Reference Angles and Unit Circle

22. §4.2: Reference Angles and Unit Circle
Assignment
Complete the Unit Circle and Worksheet 1
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§4.2: Reference Angles and Unit Circle