cosθ= −√3/4, where π≤ θ≤ 3π/2. tanβ= 3/4, where 0≤β≤ π/2. What is the exact value of sin(θ+β)?Enter your answer, as a fraction in simplified form
cos θ = - √3/4
So sin θ = -√ [ 4^2 - (-√3)^2 ] / 4 = - √[ 16 - 3 ] / 4 = - √13 / 4
tan B = 3/4
sin B = 3/5
cos B = 4/5
So
sin ( θ + B) = sinθ cosB + sinBcosθ =
(-√13/4 ) * (4/5) + ( 3/5 ) * ( - √3/4 ) =
[ -4√13 - 3√3 ]
______________
20
+23 
