Find sin θ if cot θ = -4 and cos θ < 0.

Solution:

Given, cot θ = -4 and cos θ < 0

Clearly cot θ and cos θ both are negative.

⇒ θ is an angle from II quadrant

From OA² = OB² + AB²

OA² = (-4)² + 1²

OA² = 17 ⇒ OA = √17

cot θ = Adjacent side / Opposite = -4/1

sin θ = Opposite / Hypotenuse = 1/√17

Find sin θ if cot θ = -4 and cos θ < 0.

Summary:

If cot θ = - 2 and cos θ < 0, sin θ = 1 / √17.