Question

Find the exact value of cot (theta) for an angle (theta) with sin (theta)= -1/6 and with its terminal side in Quadrant III.

Answer 1

cotθ = √35 = 5.91

Explanation:

Explanation:-

Given sin(θ) = -1/6

`cosec(theta) = (1)/(sin(theta)) = (1)/((-1)/(6) ) = -6`

We will use trigonometric formula

co sec ²θ -cot²θ =1

cot ² θ = co sec ²θ - 1

cot ² θ = (-6)² -1 = 36 -1 =35

cotθ = √35 = 5.91

Given' θ' is Quadrant III.

In third quadrant cotθ and tanθ are positive

cotθ = √35 = 5.91