Angle θ is in standard position. If tan ⁡ θ < 0 and cos ⁡ θ = - 4/5, find sin ⁡ θ.

The value found is.

sin θ = 0.6

Step-by-step explanation:

We know that the value of cosθ is given - 4/5

cosθ = - 4/5

First, lets finds the angle θ by taking inverse of cosine of - 4/5

θ = cos⁻¹ (-4/5)

θ = 143.13°

Substitute the found θ = 143.13° it in tanθ to see if satisfies the equation tanθ < 0:

tanθ < 0

tan (143.13°) < 0

-0.75 < 0

Hence the equation is satisfied.

Which means that θ is equals to 143.13° and can be used to find sinθ

sinθ = sin 143.13°

sin 143.13° = 0.6