Question

Find sin θ if cot θ = - 2 and cos θ < 0.

-1/2

- 5

square root of 5/2

square root of 5/5

Answer 1

cot theta = -2
tan theta = -1 / 2
cos theta < 0
Since tan theta and cos theta < 0, theta is in the 2nd quadrant.
sin theta = 1 / sqrt (1^2 + 2^2) = 1 / sqrt 5 = sqrt 5 / 5
It is positive because sine theta is positive in the 2nd quadrant.