1 / 9

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.

dima
Download Presentation

Trig Identities

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related