Let the angle θ satisfy sin 2θ=-4/5 and (3π/4)<θ<π . Find the value of: P=sin θ - cos θ

Question

Sidenote: Please explain your answer step-by-step, thank you! ^^

Answer 1

sin2x = -4/5

2x = -53.17 = 360-53.17 = 306.87

x = 306.84/2 = 153.435

sinx=0.4472

cosx =cos153.435 =-0.8944

sinx-cosx = 0.4472-(-0.8944) = 1.3416

use a calculator with trig functions

Answer 2

(3π/4)<θ<π

(6π/4)<(3π/4)<θ<π<2π

sin^-1(-4/5)=(-).927 radian on calculator, checks out without second solutioon

but need to make positive -.927 same as +2π-.927=5.35 radian=2θ

5.35/2=θ=2.68,,,whew,,,(3π/4)<θ<π

sinθ-cosθ=1.341