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

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(1) Answers

mattyj0300

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