Suppose cos 2A = − (2/3) , and 2A is an angle in the Third Quadrant. Then cos A =

Answer 1

π < 2A < 3π/2; π/2 < A < 3π/4, so A in 2nd Quadrant.

cosA = - √(1 + cos2A)/2 = - √(1 - 2/3)/2 = - 1/√6

Answer 2

cos(2A) = 2cos²A - 1

-2/3 = 2cos²A - 1

2cos²A = 1/3

cos²A = 1/6

cos²A = ±1/√6

Since 2A is in quadrant 3, 180° <2A <270°

So, 90° < A < 180°

Therefore, cosA < 0 So, cosA = -1/√6 = -√6/6