S UM AND D IFFERENCE I DENTITIES Objective To use the sum and difference identities for the sine, cosine, and tangent functions Page 371

Sum and Difference Identities for the Cos Function cos (  +  ) = cos  cos  – sin  sin  cos (  –  ) = cos  cos  + sin  sin  Sum and Difference Identities for the Sin Function sin (  +  ) = sin  cos  + cos  sin  sin (  –  ) = sin  cos  – cos  sin  Sum and Difference Identities for the Tan function tan (  +  ) = tan  + tan  1 - tan  tan  tan (  –  ) = tan  – tan  1 + tan  tan 

Find cos 15° cos 15° = cos (45° - 30°) = cos 45° cos 30° + sin 45° sin 30° = √2 2 ∙ √3 2 + √2 2 ∙ 1212 = √6 4 + √2 4 = √6 + √2 4

Find sin 15° sin 15° = sin (45° - 30°) = sin 45° sin 30° - cos 45° sin 30° = √2 2 ∙ √3 2 - √2 2 ∙ 1212 = √6 4 - √2 4 = √6 - √2 4

Find tan 105° tan 105° = tan ( 60° + 45°) = tan 60° + tan 45° 1 – tan 60° tan 45° = √ √3 ∙ 1 √ √3 =∙ 1 + √3 = -2 - √3

If sin  = 5/13 and cos  = 4/5, find cos (  +  ) cos (  +  ) = cos  cos  – sin  sin 

Assignment Page 375 #15 – 29, 48, 49