if pi/2 < x < pi and sinx = 2/5 then tanx = ؟

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.

This is in the second quadrant where tan is negative, so tanx = -2/√(5^{2}-2^{2}) = -2/√21

thanx for all