Calculate tg (a/2) if sin a = 3/5 and a is in the interval (pi/2, pi)?

sin a= 3/5

We know that sina = opposite/hypotenuse = 3/5

Then, the adjacent^2= 5^2 -3^2 = 25-9=16

Then the adjacent= 4

Then cos a= adj./hypotenuse= 4/5.

Now, we know that:

 tg(a/2)= sina / 1-cosa 

          = 3/5 / 1-4/5 = 3/5 / 1/5 = 3

Also tg(a/2) = (1-cosa)/sina= 1/5 /  3/5 = 1/3