Question

Find the exact value by using a half-angle identity.

sin 22.5°

Answer 1

\[\sin(22.5) = \frac{ 45 }{ 2 }\]

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

Answer 2

Ans: \[\sqrt{\frac{ 2-\sqrt{2} }{ 2 }}\]

Answer 3

there should only be a root on the numerator.

Answer 4

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 \[\frac{ \sqrt{2-\sqrt{2}} }{ 2 }\]?

Answer 5

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

Answer 6

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
\[\sqrt{(1-\cos(\pi/4))/2}\] = \[\sqrt{(1-\sqrt{2}/2)/2}\]

Answer 7

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