if -sinθ= 0.5736 and 90°≤θ≤180° , find the value of θ

Answer 1

-sinθ= 0.5736
sinθ= - 0.5736

90°≤θ≤180° <----- you are in quadrant II, in that quad the sine is positive,

so there is no solution to your equation

if you meant
sinθ= 0.5736
the angle in standard position would be 35.002° or appr 35°
so θ = 180° - 35° = 145°