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Properties of the Trigonometric Functions

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Presentation on theme: "Properties of the Trigonometric Functions"— Presentation transcript:

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

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

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

15 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.

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

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

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

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

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

25 Since θ is in quadrant II, x values are negative

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

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

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

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

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

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


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