Given that $\cos x =-3/4$ and $90^\circGiven that $\;\cos x =-\frac{3}{4}\,$ and $\,90^\circ<x<180^\circ,\,$ find $\,\tan x\,$ and $\,\csc x.$
This question is quite unusual from the rest of the questions in the chapter, can someone please explain how this question is solved? I tried Pythagorean Theorem, but no luck. Is it possible to teach me how to use the circle diagram?

You should draw a triangle!
They tell you that you're working in the second quadrant, so draw a reference triangle and label the base angle $x$.    
Since cosine is the ratio of adjacent ("over"/) to hypotenuse, we know that the length of the adjacent side is the numerator $ = 3$.
The length of the hypotenuse is the denominator $= 4$... But where does the "-" go?? 
The hypotenuse is always positive. That, and the fact that you are in the left quadrant (<=> the x-coordinate is negative) should tell you that the adjacent side should really be labeled $-3$. This will be important later, as the tangent requires the adjacent side. 
Now use the Pythagorean Theorem to find the length of the opposite side. It's $\sqrt 7$.
Then you can find tangent (opposite over adjacent), sine (opposite over hypotenuse), etc. using SOHCAHTOA.   
