Question

Evaluate the expression under the given conditions. sin(θ − ϕ); tan(θ) = 4/3 , θ in Quadrant III, sin(ϕ) = − 10/10 , ϕ in Quadrant IV

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer: -0.6

Step-by-step explanation:

First thing to do is to solve for θ and ϕ from the given information

tan(θ) = 4/3,

θ = tan-¹4/3,

θ = 53.1°

Since tan is positive in quadrant III, θ = 53.1°

Also,

sin(ϕ) = − 10/10 ,

ϕ = sin-¹-1

ϕ = 270°

If ϕ is in the fourth quadrant, that gives 360 - ϕ i.e 360 - 270 = 90°

Substituting the values of θ and ϕ into sin(θ − ϕ), we have;

Sin(53.1 - 90)

= sin (-36.9°)

= -0.6