(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)]
