Properties of the Trigonometric Functions

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Presentation transcript:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

Since θ is in quadrant II, x values are negative

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

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

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

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

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

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