1. Worksheet Key
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13.3: The Unit Circle

2. Basic Identities of Unit Circle
Section 13.3
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3. Review sin Ѳ = csc Ѳ = cos Ѳ = sec Ѳ = tan Ѳ = cot Ѳ =
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13.3: The Unit Circle

4. Reciprocal Identities Theorem
sin θ= csc θ= cos θ= sec θ= tan θ= cot θ=
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13.3: The Unit Circle

5. Right Triangles – 45°, 45°, 90°
triangles (Drawing not to scale) Radius = 1
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13.3: The Unit Circle

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

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

8. Reminder
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13.3: The Unit Circle

9. The Unit Circle Activity
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13.3: The Unit Circle

10. The Unit Circle
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13.3: The Unit Circle

11. The Unit Circle
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13.3: The Unit Circle

12. 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°
π/4
45°
√2/2
3π/4
135°
–√2/2
5π/4
225°
7π/4
315°
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13.3: The Unit Circle

13. 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°
π/6
30°
√3/2
1/2
5π/6
150°
–√3/2
7π/6
210°
–1/2
11π/6
330°
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13.3: The Unit Circle

14. 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: 30°
π/3
60°
1/2
√3/2
2π/3
120°
–1/2
4π/3
240°
–√3/2
5π/3
300°
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13.3: The Unit Circle

15. Example 1 Solve sin π/4 without a calculator 12/2/2018 11:28 PM
13.3: The Unit Circle

16. Example 2 Solve cos 7π/4 without a calculator 12/2/2018 11:28 PM
13.3: The Unit Circle

17. Your Turn Solve tan 3π/4 without a calculator 12/2/2018 11:28 PM
13.3: The Unit Circle

18. Example 3 Solve sin π/6 without a calculator 12/2/2018 11:28 PM
13.3: The Unit Circle

19. Example 4 Solve tan 11π/6 without a calculator 12/2/2018 11:28 PM
13.3: The Unit Circle

20. Example 5 Solve tan –π/3 without a calculator 12/2/2018 11:28 PM
13.3: The Unit Circle

21. Your Turn Solve tan 2π/3 without a calculator 12/2/2018 11:28 PM
13.3: The Unit Circle

22. Example 6 Solve sec 7π/4 without a calculator 12/2/2018 11:28 PM
13.3: The Unit Circle

23. Example 7 Solve csc 4π/3 without a calculator 12/2/2018 11:28 PM
13.3: The Unit Circle

24. Example 8 Solve csc –11π/6 without a calculator 12/2/2018 11:28 PM
13.3: The Unit Circle

25. Your Turn Solve cot 11π/6 without a calculator 12/2/2018 11:28 PM
13.3: The Unit Circle

26. Example 9
Solve cot π/2
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13.3: The Unit Circle

27. Example 10
Solve tan π/2
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13.3: The Unit Circle

28. Your Turn
Solve cot 4π
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13.3: The Unit Circle

29. Assignment
Worksheet
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13.3: The Unit Circle