Precalculus

Question

If
cos(θ) = − 1/11 with θ in Quadrant III, what is sin(θ)?

Answer 1

Cosine = adjacent / hypotenuse = -1 / 11.    Note that in quadrant III, opposite and adjacent are negative and hypotenuse is always positive.

Opposite side = square root of (11^2 - (-1)^2) = square root of 120.  Use the negative value because you are in Quadrant III.

Sine = opposite / hypotenuse = (- sqrt 120) / 11 = -0.996.