Cos theta = -1/2 and sin theta = -1/2

Question

Calculate all values of theta on unit circle: when cos theta = -1/2 ; and also when sin theta = -1/2

Answer 1

cos(theta) = -1/2

theta = 240 + 360n degrees where n = any integer or

120 + 360n degrees where n = any integer

or in radians

theta = 4pi/3 + 2npi where n = any integer

or 2pi/3 + 2npi where n = any integer

theta is in quadrant III or II

for sin(theta) = -1/2, theta is in quadrant III or IV

theta = 210 + 360n degrees where n= any integer

or 330 + 360n degrees where n = any integer

or in radians

theta = 7pi/6 + 2npi where n = any integer or

= 11pi/6 + 2npi where n= any integer