Copyright © 2011 Pearson, Inc.. 5.1 Fundamental Identities Goal: Use the fundamental identities to simplify trigonometric expressions.

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Presentation transcript:

Copyright © 2011 Pearson, Inc.

5.1 Fundamental Identities Goal: Use the fundamental identities to simplify trigonometric expressions.

Copyright © 2011 Pearson, Inc. Slide What you’ll learn about Identities Basic Trigonometric Identities Pythagorean Identities Cofunction Identities Odd-Even Identities Simplifying Trigonometric Expressions Solving Trigonometric Equations … and why Identities are important when working with trigonometric functions in calculus.

Copyright © 2011 Pearson, Inc. FYI

Copyright © 2011 Pearson, Inc. Slide Basic Trigonometric Identities

Copyright © 2011 Pearson, Inc. Slide Pythagorean Identities

Copyright © 2011 Pearson, Inc. Slide Cofunction Identities

Copyright © 2011 Pearson, Inc. Slide Even-Odd Identities

Copyright © 2011 Pearson, Inc. Simplification Ideas  Rewrite tan, cot, sec, and csc in terms of sin and cos.  Expand Products  Example: (1 + sin x)(1 – sin x) = 1 – sin x + sin x – sin 2 x  Factor  Example: sinxcosx – sinx = sinx(cosx – 1)  Take Square Roots  Combining Fractions

Copyright © 2011 Pearson, Inc. Slide Simplify by Rewriting

Copyright © 2011 Pearson, Inc. Slide Simplify by Expanding Products

Copyright © 2011 Pearson, Inc. Slide Simplifying by Factoring

Copyright © 2011 Pearson, Inc. Slide Simplify by Taking Square Roots

Copyright © 2011 Pearson, Inc. Slide Simplify by Combining Fractions

Copyright © 2011 Pearson, Inc. Slide Example Simplifying by Expanding and Using Identities

Copyright © 2011 Pearson, Inc. 5.1 Day 2 Fundamental Identities Goal: Solve trigonometric equations.

Copyright © 2011 Pearson, Inc. Warm Up Slide

Copyright © 2011 Pearson, Inc. Example 1: Using the Pythagorean Identity Slide

Copyright © 2011 Pearson, Inc. Example 2a: Solving Trigonometric Equations by Factoring Slide

Copyright © 2011 Pearson, Inc. Example 2b: Solving Trigonometric Equations by Factoring Slide

Copyright © 2011 Pearson, Inc. Example 2c: Solving Trigonometric Equations by Factoring Slide