Angle θ is in standard position. if sin (θ) = - 1/3, and π < θ < 3π/2, find cos (θ).

A. - (2√2) / 3

B. 4/3

C. 2√2/3

Use pythagorean theorem:

sin^2 + cos^2 = 1

(-1/3) ^2 + cos^2 = 1

1/9 + cos^2 = 1

cos^2 = 8/9

cos = + - sqrt (8) / sqrt (9) = + - 2sqrt (2) / 3

Determine whether cos is positive or negative by looking at which quadrant the angle is in.

pi < theta this is 3rd quadrant where x or cos is negative

Therefore cos (theta) = - 2sqrt (2) / 3