half angle formula

Question

Given sin (a)= 8/9 and pi/2 <a<pi

Find the exact value of sin (a/2)

do not use decimals 

sin (a/2)=?

Answer 1

Since a is in the second quadrant, cos(a) = -sqrt(17)/9, for 8, sqrt(17) and 9 right triangle.

Since a/2 is in the first quadrant,

sin(a/2)

= sqrt[(1/2)(1-cos(a))]

= sqrt[(1/2)(1+sqrt(17)/9)] <==Answer

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Attn: You can simplify the answer further.