Question

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

Answer 1

Answer:

-2√2/3 is the correct answer. :))

Step-by-step explanation:

Answer 2

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 < 3pi/2 ---> this is 3rd quadrant where x or cos is negative

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