Question

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

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Answer 1

Answer:

Option C

Step-by-step explanation:

Please see attached picture for full solution.

x has a negative value since it lies on the left side of the y axis. (Hence we reject positive √35)

Answer 2

Answer:

C. sqrt(35)

Step-by-step explanation:

sin(theta) = opposite/hypotenuse

= -1/6

adjacent = sqrt(6² - 1²)

= sqrt(35)

tan(theta) = opposite/adjacent

Positive in Quadrant III

cot(theta) = adjacent/opposite

= sqrt(35) ÷ 1

= sqrt(35)