Question

if sin x = 2/3 and sec y = 5/4 where x and y lie between 0 and π/2 evaluate sin(x + y)

Answer 1

ok... you need to find cos y

If sec (y) = 5/4

then take the reciprocal of both sides to fins cos(y)

( since sec = 1/cos)

so cos(y) = 4/5 (a 1st quadrant value given the domain)

so now you need the expansion of

sin(x + y) = sin(x)cos(y) + cos(x) sin(y)

substitute your known ratios sin(x) = 2/3 and cos(x) = 4/5

and then just evaluate.