Given tan t = 2/3 and that pi <= t <= 3pi/2. Find exact value for each of the following: a) sec t
b) cos t
c) sin t
d) csc t
e) cot t

well, first off let's notice something about angle "t", is between π and 3π/2, or namely the III Quadrant, where both "x" or adjacent side as well as "y" or opposite side are negative.

something else noteworthy is that, the hypotenuse is just a radius length and thus is never negative.

tube or goog would be a great resource to with that question