Maths trigonometry help?!?

If sin(Theta) = 3/4 and cos(theta)<0, find the exact value of tan(Theta)

Thanks and please explain

sin(theta) = 3/4
sin^2(theta) = 9/16
=> we know that sin^2(theta) + cos^2(theta) = 1
=> cos^2(theta) = 1-9/16
=> cos^2(theta) = 7/16
=> cos(theta) = -sqrt(7)/4 or sqrt(7)/4
it is given that cos is negative so cos(theta) = -sqrt(7)/4
=> tan(theta) = sin(theta)/cos(theta) = (3/4)/ -sqrt(7)/4
= -3/sqrt(7)