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Exploring Trigonometric Identities and Formulas for Proofs

Learn new trig identities, methodology, and proof structures, including exciting calculations and rules for sine, cosine, and tangent. Practice proving trigonometric expressions and explore additional trig rules.

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Exploring Trigonometric Identities and Formulas for Proofs

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  1. Trig Identities

  2. What is to be learned? • Some new trig formulae • Correct methodology and structure for proofs

  3. =(Sinx)2 Squaring Sinx Sinx X Sinx Written as sin2x

  4. Some exciting calculations sin2(30) + cos2(30) (sin30)2 + (cos30)2 Repeat for 75.30 Rule sin2x+ cos2x = 1

  5. Two “new” rules sin2x + cos2x = 1 so sin2x = and cos2x = 1-cos2x 1-sin2x

  6. Almost as exciting sin450÷ cos450 tan450? Repeat for any angle Rule sinx= tanx cosx

  7. sin2x + cos2x = 1 ( ) sin2x = 1- cos2x cos2x = 1 - sin2x Proof Type Questions Prove 2sin2x+ 2cos2x = 2 LHS 2sin2x+ 2cos2x = 2(sin2x + cos2x) = 2 X 1 = 2 Sinx = tanx Cosx =RHS QED

  8. More Trig Rules sin2x + cos2x = 1 also sin2x = 1-cos2x and cos2x = 1- sin2x Tanx = Sinx Cosx

  9. sin2x + cos2x = 1 ( ) sin2x = 1- cos2x cos2x = 1 - sin2x Prove sin2x = tan2x LHS sin2x sin2x Sinx = tanx 1 – sin2x Cosx 1 – sin2x cos2x = tan2x =RHS QED

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