Cot = adjacent / opposite = 2/3 but it lies in the 4th quadrant so 2/-3 Sin = opposite / hypotenuse , you have it as x/2 So you have the hypotenuse and the opposite is -3 so -3/2 Sin(-3/2) = -sin (3/2) Alternative form : -0.997495
cos x / sin x = 2 / 3 2 sin x = 3 cos x sin x = 3 cos x / 2 sin² x + cos² x = 1 9 cos² x / 4 + cos² x = 1 / * 4 9 cos² x + 4 cos² x = 4 13 cos² x = 4 cos x = 2 / √13 sin ( x/2 ) = √ [( 1 - cos x )/ 2] = √ [( 1 - 2/√13 ) / 2] = √(√13 - 2 )/(2√13) or sin ( x/2 ) ≈ 0.471858
