Please help Evaluate sintheta phi if sintheta 38 theta is

Please help

Evaluate sin(theta + phi) if sin(theta) = 3/8, theta is in quadrant II, sin(phi) = 4/5 and phi is in quadrant I. Show your work; calculator work will not be accepted. You may leave your answer in unsimplified form.

Solution

sin theta= 3/8

here opposite=3   and hypotenuse=8

adjacent= sqrt(8²-3²) = sqrt55

cosine is negative in second quadrant

cos theta= adjacent/hypotenuse = -(sqrt55)/8

sin phi= 4/5

adjacent=sqrt(5²-4²) = 3

cos pji=3/5

sin(theta + phi) = sin theta cos phi + cos theta sin phi

                      = (3/8)(3/5)+ (-sqrt55/8)(4/5) = (9-4sqrt55)/40