Alright, lets gets started.
We have given two things, cot Θ= - 4 and cos Θ < 0
Means both cot and cos are negative.
So, the quadrant in which Θ lies , is 2nd.
Because in 2nd quadrant, cos and cot both are negative.
Please refer the diagram attached.
Cot Θ = -4 means tan Θ = - 1/4
Means two sides, opposite = 1
adjacent = -4
We could find hypotenuse by using Pythagorean theorem.
Hypotenuse = sqrt (1^2 + -4^2) = sqrt (1+16)
Hypotenuse = √17
sin Θ = opposite / hypotenuse
sin Θ = 1/√17
Multiply and divide with √17
sin Θ = 1/√17 * √17/√17
sin Θ = √17/17 : Answer
Hope it will help :)
