This is statement is FALSE. Since the tangent of A is negative, the possible angles can be in the second quadrant (between 90 and 180 degrees) and the third quadrant (between 180 and 270 degrees). But, the tangent of `1/sqrt3` corresponds to the acute angle of 30 degrees, or `pi/6` radians. This is the reference angle for angles 180 - 30 = 150 degrees (`(5pi)/6` radians) in the second quadrant and 180 + 30 = 210 degrees
(`(7pi)/6 ` radians) in the third quadrant. The angles indicated in the question have tangent of `-sqrt(3)` .
Isn't tan negative in quadrants 2 and 4 though? Isn't that what the CAST rule tells us - cos is positive in 4, all positive in 1, sin is positive in 2, and tan is positive in 3; therefore, tan is positive in 1 and 3 - hence it is negative in 2 and 4? Am I wrong?