SOLUTION: Find the exact values of sin(2u), and cos(2u), and tan(2u) using the double angle formulas. cot(u)=-5, 3pi/2 < u < 2pi

 tells us that angle u is in
the fourth quadrant. 

Since  and we are given that
, we consider the  as ,
the we can make the numerator be the adjacent side of +5 and 
the denominator be -1.   

So we draw a right triangle in the fourth quadrant whose adjacent
side is +5 and whose opposite side is -1.  [We knew to consider
the -5 as  and not  because
+5 goes to the right and -1 goes down.] 

The angle u is represented by the red arc drawn counterclockwise
from the right side of the x-axis to the terminal side which is
the hypotenuse of the right triangle.

The hypotenuse is calculated from the Pythagorean theorem:




 <-- the hypotenuse is always positive!






Now we use some double angle identities:







We could use the formula for tan(2u), but it's easier
to use 



Edwin