Tyler

2cos^2(X) - 3sin(X) = 02(1 - sin^2(X)) - 3sin(X) = 02 - 2sin^2(X) - 3sin(X) = 0-2sin^2(X) - 3sin(X) + 2 = 0-2sin^2(X) - 4sin(X) + sin(X) + 2 = 0-2sin(X)(sin(X) + 2) + 1(sin(X) + 2) = 0(-2sin(X) + 1)(sin(X) + 2) = 0Solve First:-2sin(X) + 1 = 0sin(X) = -1/-2 = 1/2Quadrant 1, 2Ref. Angle PI/6X1 = PI/6X2 = PI - PI/6 = 5PI/6Solve Second:sin(X) + 2 = 0sin(X) = -2CANNOT ANSWERX = PI/6, 5PI/6You could have possibly went sin(X) = -1/2 or sin(X) = 1/-2 rather than sin(X) = -1/-2 = 1/2 ;)