SOLUTION: Give sin(a) =8/9, pi/2< a < pi, Find the exact value of sin(a/2) I tried solving it but I got stuck in some part. Here is my step for solving it. Do pythagoream theorem to

Question 1007340: Give sin(a) =8/9,
pi/2< a < pi,
Find the exact value of sin(a/2)
I tried solving it but I got stuck in some part.
Here is my step for solving it.
Do pythagoream theorem to find cos (a)
sin(a)=8/9 = y/r
y=8, r=9
r^2=x^2+y^2
9^2=x^2+8^2
81=x^2+64
sqrt(17)=x
cost=x/r=sqrt(17)/9
use double angle formula, sin(x/2)= +/- sqrt((1-costx)/2)
sin(x/2)= +/- sqrt((1-sqrt((17)/9))/2)
sin(x/2)= +/- sqrt((9/9-sqrt(17)/9))/2), I am stuck here.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If , then . So you are correct there.

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Start with .

Multiply every side by to get

The angle is larger than but smaller than . This places angle in quadrant 1. So is positive. So we only use the "plus" version of the formula (NOT the minus, NOT the plus/minus)

Exact value

Approximate value (use a calculator)

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