Question

If
sin(x) = 1/3 and sec(y) = 13/12
, where x and y lie between 0 and π/2, evaluate the expression using trigonometric identities. (Enter an exact answer.)
sin(x + y)

Answer 1

since both x and y are in quadrant I, everything will stay positive
make sketches of right-angled triangles for each case

from sinx = 1/3, cosx = √8/3

from secy = 13/12 ---> cosy = 12/13
then siny = 5/13

sin(x+y) = sinxcosy + cosxsiny
= (1/3)(12/13) + (√8/3)(5/13)
= (12+5√8)/39 or
= (12 + 10√2)/39

Answer 2

please correct cosx = - square 8/3