Determine quad.

(a) Determine the Quadrant in which (U/2) lies 

(b) find the exact values of sin(u/2), cos(u/2) and tan (u/2)

cot(u)= -1/3, 3pi/2 <U< 2Pi..........then u/2 will fall into the 2nd quadrant

If the cotangent is -1/3, then  r = √[!1^2 + 3^2]  = √10

And the sin of u  = -3/√10      and the cos of  u  =   1/√10

So.....

tan (u/2) =  sin u / [ 1 + cos u]  = [ -3/√10] / [ 1 + 1√10] =   [-3√10] / [  (√10 + 1) / √10]  =  [-3] / [  √10 + 1]

And

sin (u/2) =  √ [(1 - cos u) / 2]  = √ [(1 - 1/√10)/ 2 ]   = √ [ (√10 - 1) / (2√10)] 

cos(u/2)  = -√ [ (1 + cos u) / 2 ]  = -√ [  [(1 + 1/√10)/ 2 ]  =  - √ [(√10 + 1) / (2√10)]