Question

cosθ=-√2/3 , where π≤θ≤3π/2 .

tanβ=4/3 , where 0≤β≤π/2 .

What is the exact value of sin(θ+β)?

Enter your answer, as a fraction in simplified form,

sin(θ+β) =

Answer 1

Answer:

Cosθ= -√2/3

Sinθ= -√7/3

tanβ= 4/3

Sinβ= 4/5

Cosβ= 3/5

sin(θ+β) = sin(θ)cos(β)+cos(θ)sin(β)

(-√7/3)(3/5) + (-√2/3)(4/5)

-√7/5 - 4√2/15