Please be sure to do all four parts Homework Section 74 Home

Please be sure to do all four parts

Homework: Section 7.4 Homework Score 0 of 1 pt X 7.5.33 Find the exact value of each of the following under the given conditions: 2153 B

Solution

sin alpha=5/13

Here opposite=5    and hypotenuse=13

adjacent=sqrt(13²-5²)= 12

cos alpha=12/13

cos beta=2 sqrt53/53

here adjacent=2 sqrt53    and hypotenuse=53

opposite= sqrt(53²-(2sqrt53)²) = sqrt 2597=7sqrt53

sin beta= -7sqrt53/53

sin(alpha+ beta)= sin alpha cos beta + cos alpha sin beta= (5/13)(2sqrt53/53)+(12/13)(-7sqrt53/53)

                                                                                                  = -74sqrt53/689

cos (alpha + beta) = cos alpha cos beta - sin alpha sin beta=(12/13)(2sqrt53/53)-(5/13)(-7sqrt53/53)

                                                                                                      = 59sqrt53/ 689

tan(alpha+ beta)=sin(alpha+beta)/cos(alpha+beta)= -74/59

sin(alpha- beta)=sin alpha cos beta - cos alpha sin beta= 94sqrt53/689