suppose sinx=1/5, cosy=2/3, and x and y are in the first quadrant. determine sin (x+y)

Answer 1

if sin a = 1/5
then cos a = sqrt(1 - 1/25)
= sqrt (24/25) = (2/5) sqrt 6

if cos b = 2/3
then sin b = sqrt ( 1 - 4/9)
= (1/3) sqrt 5

then use
sin (a+b) = sin a cos b + cos a sin b