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Trig Identities

Trig Identities. What is to be learned?. Some new trig formulae Correct methodology and structure for proofs. =(Sinx) 2. Squaring Sinx Sinx X Sinx Written as sin 2 x. Some exciting calculations sin 2 (30) + cos 2 (30). (sin30) 2 + (cos30) 2. Repeat for 75.3 0.

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Trig Identities

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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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