1. Properties of the Trigonometric Functions
Section 6.3
Properties of the Trigonometric Functions
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

2. Determine the domain and the range of the trigonometric functions.
Objectives
Determine the domain and the range of the trigonometric functions.
Determine the period of the trigonometric functions.
Determine the signs of the trigonometric functions in a given quadrant.
Find the values of the trigonometric functions using fundamental identities.
Find the exact values of the trigonometric functions of an angle given one of the functions and the quadrant of the angle.
Use even-odd properties to find the exact values of the trigonometric functions.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

3. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

4. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

5. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

6. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

7. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

8. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

9. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

10. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

11. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

12. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

13. Therefore, this angle must lie in quadrant II.
If sin  > 0 and cos  < 0, name the quadrant in which the angle  lies.
For sin  > 0 the y value must be positive so the angle must be in quadrant I or II.
For cos  < 0 the x value must be negative so the angle must be in quadrant II or III.
Therefore, this angle must lie in quadrant II.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

14. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

15. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

16. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

17. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

18. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

19. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

20. θ
P(x,2)
r = 5
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

21. Since θ is in quadrant II, x values are negative

22. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

23. P(-1,-3) θ
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

24. Since sin θ < 0, csc θ is negative.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

25. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

26. Find the exact value of: cos (60°) (b) sin (390°) (c) tan
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

27. Homework 6.3: # 5-10 all, 11-37 odd, 43, 45, 59-83 odd
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.