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5.1 Fundamental Identities

5.1 Fundamental Identities. Statements like “ ” and “ ” are trigonometric identities because they are true for all values of the variable for which both sides of the equation are defined. The set of all such values is called the domain of validity of the identity.

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5.1 Fundamental Identities

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  1. 5.1 Fundamental Identities • Statements like “ ” and “ ” are trigonometric identities because they are true for all values of the variable for which both sides of the equation are defined. • The set of all such values is called the domain of validity of the identity. • Basic Trigonometric Identities • Some trigonometric identities follow directly from the definitions of the six basic trigonometric functions. • These basic identities consists of the reciprocal identities and the quotient identities.

  2. Basic Trigonometric Identities • Reciprocal Identities

  3. Basic Trigonometric Identities • Quotient Identities

  4. Basic Trigonometric Identities • Pythagorean Identities

  5. Using Identities • Find and if and

  6. Cofunction Identities

  7. Odd-Even Identities

  8. Using More Identities • If , find

  9. Simplifying by Factoring and Using Identities • Simplify the expression

  10. Simplifying by Expanding and Using Identities • Simplify the expression

  11. Simplifying by Combining Fractions and Using Identities • See Example 5 on p. 448 – 449.

  12. Solving a Trigonometric Equation • See Example 6 and Example 7 on p. 449 – 450.

  13. More Practice!!!!! • Homework – Textbook p. 451 – 452 #1 – 31 ODD.

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