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

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