Mat 161 PreCalculus

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Mat 161 - PreCalculus

• Proofs ofTrigonometric Identitites
• (Section 6.1)

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Trigonometric Identities

• Observations/Identities
• 1) sin2? cos2? 1 5) sec? 1/cos?
• 2) tan2? 1 sec2? 6) cot? 1/tan?
• 3) 1 cot2? csc2? 7) tan? sin?/cos?
• 4) csc? 1/sin? 8) cot?
  cos?/sin?

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Trigonometric Identities

• Observations/Identities
• 9) sin(-?) - sin? 10) csc(-?) -csc?
• 11) tan(-?) -tan? 12) cot(-?) -cot?
• 13) cos(-?) cos? 14) sec(-?) sec?

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Trigonometric Identities

• Def A trigonometric identity is an equation that
  holds for all real numbers in the domain of the
  expressions in the equation.
• Example tan(x) sin(x)/cos(x)
• Def To verify that an equation is an identity,
  we must show that one side is equal to the other
  side.

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Trigonometric Identities

• Verify the identity
• cosx cscx cotx

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Trigonometric Identities

• Verify the identity
• cotx secx sinx 1

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Trigonometric Identities

• Verify the identity
• cot(-x) sinx -cosx

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Trigonometric Identities

• Verify the identity
• cos2x sin2x 2cos2x - 1

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Trigonometric Identities

• Verify the identity

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Trigonometric Identities

• Verify the identity

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Trigonometric Identities

• Verify the identity

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Trigonometric Identities

• Verify the identity

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Trigonometric Identities

• Verify the identity

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Trigonometric Identities

• Verify the identity

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Trigonometric Identities

• Verify the identity

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Trigonometric Identities

• Verify the identity

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Trigonometric Identities

• Verify the identity

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Trigonometric Identities

• Verify the identity

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Trigonometric Identities

• Reference
• Algebra and Functions
• Blitzer
• 3rd Edition