If sin θ = negative square root 3 over 2 and π < θ < 3 pi over 2, what are the values of cos θ and tan θ?

Sin(teta) = -√3/2

pi<teta<3pi/2

because of range of pi we can conclude that teta is in third quadrant of x-y coordinate system which will determine us what is the sign of cos(teta) and tan(teta)
cos(teta) = √(1-sin^2(teta)) = 1/2
but because teta is in third quadrant, cos(teta) has to be negative which means:
cos(teta) = -1/2

tan(teta) = sin(teta)/cos(teta) = √3

tan of an angle that is in third quadrant is positive which is what we got.

Answer is:
cos(teta) = -1/2
tan(teta) = √3