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Section 14-2: Trigonometric Identities

CHAPTER 14: PROPERTIES OF TRIGONOMETRIC AND CIRCULAR Functions. Section 14-2: Trigonometric Identities. Objective. Given a trigonometric equation, prove that it is an identity. Purposes. There are two purposes for learning how to prove identities.

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Section 14-2: Trigonometric Identities

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  1. CHAPTER 14: PROPERTIES OF TRIGONOMETRIC AND CIRCULAR Functions Section 14-2: Trigonometric Identities

  2. Objective • Given a trigonometric equation, prove that it is an identity.

  3. Purposes • There are two purposes for learning how to prove identities. • To learn the relationships among the functions. • To learn to transform one trigonometric expression into another equivalent form, usually by simplifying it.

  4. agreement • To prove that an equation is an identity, start with one member and transform it into the other.

  5. Example • Prove:

  6. Notes • When working on identities, we must only work on one side of the equal sign!!!

  7. Example • Prove:

  8. Example • Prove:

  9. Example • Prove:

  10. Steps in Proving Identities • Pick the member you wish to work with and write it down. Usually it is easier to start with the more complicated member. • Look for algebraic things to do: • If there are two terms and you want only one: • Add fractions • Factor something out. • Multiply by a clever form of 1. • To multiply a numerator or denominator by its conjugate. • To get a desired expression in a numerator or denominator. • Do any obvious algebra such as: • Distributing • Squaring • Multiplying polynomials • Look for trigonometric things to do: • Look for familiar trigonometric expressions. • If there are squares of functions, think of the Pythagorean properties. • Keep looking at the answer to make sure you are headed in the right direction.

  11. HOMEWORK: PAGE 811 #1-33 ODD

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