If sinx=1/3 and π/2<x<π , find the EXACT value of sin(x+π/6)

Answer 1

Since x is in quadrant 2, cosx is negative. cosx = -√[1-(1/3)²] = -2√2/3

sin(x + π/6) = (sinx)cos(π/6) + (cosx)sin(π/6) = (1/3)(√3/2) - (2√2/3)(1/2) = (√3 - 2√2) / 6

Answer 2

sin x = 1/3 → cos x = 2√2 / 3

sin (x + π/6)

sin x cox π/6 + cos π/6 sin x

(1 / 3)(√3 / 2) + (2√2 / 3)(1 / 3)

Can you simplify and answer?