when pi/2<thetha<3pi/4, what can tan of thetha be

Question

can someone please explain why the answer can be -8

Answer 1

Here is an intuitive way to look at this (not a formal proof):

 

This puts you in quadrant II where x is negative and y is positive, so tanθ is negative. Just above π/2, tanθ is negative but with a large absolute value.  At 3π/4,

 

tan(3π/4) = -1

 

So over the interval (π/2, 3π/4), tanθ varies from a negative number of large absolute value, and approaches -1 as θ approaches 3π/4.  In between those values, you will encounter a θ such that tanθ = -8.