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half angle formula

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)=?
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1 Answer

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.