Question

If sin⁡ θ=−4/5, and 270°<θ<360°, what is tan θ?

Answer 1

tan ⁡ θ = -4/3.

Explanation:

The sine is (opposite/hypotenuse) is negative in this Quadrant ( Quadrant IV ) and so is the tan.

The value of the adjacent side is √(-4)^2 + 5^2) = 3.

So tan ⁡ θ = opposite/ adjacent side = -4/3.

Answer 2

-4/3

Explanation:

since sin θ=−4/5 then θ = -53° 7' 48.37"

and by adding 360 to this negative angle to make it at the least positive solution and as θ is between 270° and 360°

θ = 306° 52' 11.63" so you can find any trig identity after that

then tan(306° 52' 11.63" ) = -4/3