Sum and Difference

Sum and Difference Formulas for Sine and Cosine 

                Cos(α+β)=cosαcosβ-sinαsinβ

                Cos(α-β)=cosαcosβ+sinαsinβ

                Sin(α+β)=sinαcosβ+cosαsinβ

                Sin(α-β)=sinαcosβ-cosαsinβ

To set up sum and differences, we can use special values of 30˚, 60˚, and 45˚

1)       Find the exact value of cos 15˚

Cos15˚=cos(45˚-30˚)                               Replace 15 with 45-30

=cos45cos30+sin45sin30                       plug values into the formula

=(√2/2)(√3/2)+(√2/2)(1/2)                     replace special values√

=(√6/4)+(√2/4)                                         Simplify

=(√6+√2)/4

2)      Find exact value of cos 75˚

Cos75=cos(45+30)                                  Replace 15  with 45+30

=cos45cos30-sin45sin30                       plug values into the formula

=(√2/2)(√3/2)-(√2/2)(1/2)                     replace special values

=(√6/4)-(√2/4)                                         Simplify

=(√6-√2)/4

3)      Find exact value of sin 75˚

Sin75=sin(45+30)                                    Replace 75 with 45+30

=sin45cos30+cos45sin30                       plug values into the formula

=(√2/2)(√3/2)+(√2/2)(1/2)                     replace special values

=(√6/4)+(√2/4)                                         Simplify

=(√6+√2)/4

Jenna Roussel