Sum and Difference Identities 5.4 Day 1 Sum and Difference Identities

Sum and Difference Identities Objective To use the sum and difference identities for the sine and cosine functions

Sum and Difference Identities for the Sin Function 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

1) cos 50º cos 10° - sin 50º sin 10° cos (50º + 10°) cos (60°) 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) sin2xcosx – sinxcos2x sin (2x – x) sin x   3)   1

4) cos4xcos3x + sin4xsin 3x cos (4x – 3x) cosx

Find the exact value of cos 75° 5. cos 75° = cos (45° + 30°) = cos 45° cos 30° – sin 45° sin 30°       =             =     =

6. Sin 285° = sin (225° + 60°) = sin 225° cos 60° + cos 225° sin 60° =   (Quickest to convert to a degree) 6. Sin 285° = sin (225° + 60°) = sin 225° cos 60° + cos 225° sin 60°         =           =     =

7. cos 195° = cos (225° – 30°) = cos 225° cos 30° + sin 225° sin 30° = YOU TRY   7. cos 195° = cos (225° – 30°) = cos 225° cos 30° + sin 225° sin 30°       =             =     =

HOMEWORK: 5.4 Day 1 worksheet