SUM AND DIFFERENCE IDENTITIES Objective To use the sum and difference identities for the sine and cosine functions
Sum and Difference Identities for the Cos Function cos (a + b) = cos a cos b – sin a sin b cos (a – b) = cos a cos b + sin a sin b Sum and Difference Identities for the Sin Function sin (a + b) = sin a cos b + cos a sin b sin (a – b) = sin a cos b – cos a sin b
USE THE SUMS AND DIFFERENCE FORMULAS TO SIMPLIFY TO A SINGLE TRIG FUNCTION. FIND THE EXACT VALUE IF POSSIBLE. (THESE ARE THE EXPANDED FORM, CONDENSE) EXAMPLES: 1) cos 50º cos 10° - sin 50º sin 10° cos (50º + 10°) cos (60°)
2) sin 2 xcosx – sinxcos 2 x sin (2 x – x) sin x 3) 1
4) cos 4 xcos 3 x + sin 4 xsin 3 x cos (4 x – 3 x) cosx
Find the exact value of cos 75° 5. cos 75° = cos (45° + 30°) = cos 45° cos 30° – sin 45° sin 30° = = =
(Quickest to convert to a degree) 6. Sin 285° = sin (225° + 60°) = sin 225° cos 60° + cos 225° sin 60° = = =
YOU TRY 7. cos 195° = cos (225° – 30°) = cos 225° cos 30° + sin 225° sin 30° = = =