find the exact value under the given conditions sin817 pi2

find the exact value under the given conditions.

sin()=8/17, pi/2< ; cos=20/29, 0<<pi/2 Find sin(-)

Solution

sin(alpha)=8/17                                                pi/2< alpha<pi

here opposite=8   hypotenuse=17

adjacent=sqrt(hypotenuse²-opposite²) =   sqrt(17²-8²)=15

In second quadrant cosine is negative

Therefore cos alpha=-15/17

            cos beta= 20/29

adjacent=20       hypotenuse=29

opposite = sqrt(hypotenuse²-adjacent²) = sqrt(29²-20²)= 21

sin beta=21/29

sin(alpha-beta) =   sin alpha cos beta   - cos alpha sin beta = (8/17)(20/29)-(-15/17)(21/29)

                                                                                                      = (160/493)+ (315/493)= 475/493