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

Answer:

 cotθ = √35 = 5.91

Step-by-step explanation:

Explanation:-

Given sin(θ) = -1/6

         $cosec(theta) = \frac{1}{sin(theta)} = \frac{1}{\frac{-1}{6} } = -6$

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