## anonymous 3 years ago Find the exact value by using a half-angle identity. sin 22.5°

1. abb0t

$\sin(22.5) = \frac{ 45 }{ 2 }$ use ur double angle formula $\sin(\frac{ 1 }{ 2 }*x) = 0 \pm \sqrt{\frac{ 1-\cos(x) }{ 2 }}$ where x = 45.

2. abb0t

Ans: $\sqrt{\frac{ 2-\sqrt{2} }{ 2 }}$

3. abb0t

there should only be a root on the numerator.

4. anonymous

Ok I got that I had to plug in 45 for the x's in the formula and I got that cos 45= $\frac{ \sqrt{2} }{ 2 }$ how did you get $\frac{ \sqrt{2-\sqrt{2}} }{ 2 }$?

5. anonymous

actually $\frac{ \sqrt{2-\sqrt{2}} }{ 2 }$ is not an option for answers

6. anonymous

incorrect, you must convert 22.5 degrees to radians before using the half-angle formula 22.5 degrees = pi/8 radians put it into the formula and get $\sqrt{(1-\cos(\pi/4))/2}$ = $\sqrt{(1-\sqrt{2}/2)/2}$

7. anonymous

the answer simplifies to $1/2 \sqrt{2-\sqrt{2}}$