CHAPTER 7: Trigonometric Identities, Inverse Functions, and Equations

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CHAPTER 7: Trigonometric Identities, Inverse Functions, and Equations 7.1 Identities: Pythagorean and Sum and Difference 7.2 Identities: Cofunction, Double-Angle, and Half-Angle 7.3 Proving Trigonometric Identities 7.4 Inverses of the Trigonometric Functions 7.5 Solving Trigonometric Equations Copyright © 2009 Pearson Education, Inc.

7.1 Identities: Pythagorean and Sum and Difference State the Pythagorean identities. Simplify and manipulate expressions containing trigonometric expressions. Use the sum and difference identities to find function values. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Basic Identities Copyright © 2009 Pearson Education, Inc.

Pythagorean Identities Recall the equation of a unit circle in the xy-plane Copyright © 2009 Pearson Education, Inc.

Pythagorean Identities We can develop two other Pythagorean identities. Copyright © 2009 Pearson Education, Inc.

Pythagorean Identities Equivalent Forms Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Example Factor and simplify Solution: Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Example Simplify each of the following trigonometric expressions. Solution: Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Example Solution continued: Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Example Add and simplify Solution: Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Example Express as a trigonometric function of  without using radicals by letting x = 3 tan Assume that 0 <  < π/2. Then find sin  and cos . Solution: Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Example Solution continued: Copyright © 2009 Pearson Education, Inc.

Sum and Difference Identities Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Example Find cos (5π/12) exactly. Solution: Copyright © 2009 Pearson Education, Inc.