if pi/2 < x < pi and sinx = 2/5 then tanx = ؟
This is in the second quadrant where tan is negative, so tanx = -2/√(52-22) = -2/√21
I always draw the right angled triangle for these.
x is one of the acute angles
2 is the opposite side, 5 is the hypotenuse.
Get the other side using pythagoras' Theorum
then read tanx of the triangle.
plus as Alan said it is in the second quad so it is negative.