2. 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
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3. 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.
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4. Copyright © 2009 Pearson Education, Inc.
Basic Identities
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5. Pythagorean Identities
Recall the equation of a unit circle in the xy-plane
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6. Pythagorean Identities
We can develop two other Pythagorean identities.
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7. Pythagorean Identities
Equivalent Forms
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8. Copyright © 2009 Pearson Education, Inc.
Example
Factor and simplify
Solution:
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9. Copyright © 2009 Pearson Education, Inc.
Example
Simplify each of the following trigonometric expressions.
Solution:
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10. Copyright © 2009 Pearson Education, Inc.
Example
Solution continued:
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11. Copyright © 2009 Pearson Education, Inc.
Example
Add and simplify
Solution:
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12. 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:
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13. Copyright © 2009 Pearson Education, Inc.
Example
Solution continued:
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14. Sum and Difference Identities
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15. Copyright © 2009 Pearson Education, Inc.
Example
Find cos (5π/12) exactly.
Solution:
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