1. Page 796 12) y = 6, DE = 7, FG = 8 13) x = 4.2, JL = 14.2, MN = 13 14)
x = 40/11, UV = 13, WZ = 161/11
16)
x = 47/5, AC = 72/5, AE = 12
17)
y = 14.3, HL = 24.3, NL = 27
18)
x = 11.5, PT = 13.5, PR = 9
19)
𝟐 𝟐𝟏
20)
10.5
21)
𝟒 𝟏𝟎
25)
x = 8, y = 𝟔 𝟑
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11-8: The Unit Circle

2. 10/21/2019 2:26 AM
11-8: The Unit Circle

3. 10/21/2019 2:26 AM
11-8: The Unit Circle

4. Quiz
When done, turn it in to the inbox and pick up a paper plate, ruler, and two or three markers
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11-8: The Unit Circle

5. Basic Identities of Unit Circle
Section 11-8
Revised ©2014
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11-8: The Unit Circle

6. Review sin Ѳ = cos Ѳ = tan Ѳ = 10/21/2019 2:26 AM
11-8: The Unit Circle

7. Right Triangles – 45°, 45°, 90°
triangles (Drawing not to scale) Radius = 1
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11-8: The Unit Circle

8. Right Triangles – 30°, 60°, 90°
triangles (Drawing not to scale) Radius = 1
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11-8: The Unit Circle

9. Right Triangles – 60°, 30°, 90°
triangles (Drawing not to scale) Radius = 1
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11-8: The Unit Circle

10. Reminder
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11-8: The Unit Circle

11. The Unit Circle Activity
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11-8: The Unit Circle

12. The Unit Circle
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11-8: The Unit Circle

13. The Unit Circle
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11-8: The Unit Circle

14. The Unit Circle - π/4 Family
cos Ѳ
sin Ѳ
Reference Angle: 45°
π/4
45°
3π/4
135°
5π/4
225°
7π/4
315°
Reference Angle: 45°
45°
√2/2
135°
–√2/2
225°
315°
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11-8: The Unit Circle

15. The Unit Circle - π/6 Family
cos Ѳ
sin Ѳ
Reference Angle: 30°
π/6
30°
5π/6
150°
7π/6
210°
11π/6
330°
Reference Angle: 30°
30°
√3/2
1/2
150°
–√3/2
210°
–1/2
330°
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11-8: The Unit Circle

16. The Unit Circle - π/3 Family
cos Ѳ
sin Ѳ
Reference Angle: 60°
π/3
60°
2π/3
120°
4π/3
240°
5π/3
300°
Reference Angle: 60°
60°
1/2
√3/2
120°
–1/2
240°
–√3/2
300°
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11-8: The Unit Circle

17. Example 1 Solve sin 45° without a calculator 10/21/2019 2:26 AM
11-8: The Unit Circle

18. Example 2 Solve cos 315° without a calculator 10/21/2019 2:26 AM
11-8: The Unit Circle

19. Example 3 Solve tan 135° without a calculator 10/21/2019 2:26 AM
11-8: The Unit Circle

20. Your Turn Solve tan 225° without a calculator 10/21/2019 2:26 AM
11-8: The Unit Circle

21. Example 4 Solve sin 30° without a calculator 10/21/2019 2:26 AM
11-8: The Unit Circle

22. Example 5 Solve cos 210° without a calculator 10/21/2019 2:26 AM
11-8: The Unit Circle

23. Example 6 Solve tan 300° without a calculator 10/21/2019 2:26 AM
11-8: The Unit Circle

24. Example 7 Solve tan 30° without a calculator 10/21/2019 2:26 AM
11-8: The Unit Circle

25. Your Turn Solve tan 150° without a calculator 10/21/2019 2:26 AM
11-8: The Unit Circle

26. Example 7 Solve tan 90° without a calculator 10/21/2019 2:26 AM
11-8: The Unit Circle

27. Example 8 Solve tan 360° without a calculator 10/21/2019 2:26 AM
11-8: The Unit Circle

28. Your Turn Solve tan 270° without a calculator 10/21/2019 2:26 AM
11-8: The Unit Circle

29. Assignment
Worksheet
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11-8: The Unit Circle