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marasofia1616
Find the exact value by using a half-angle identity. sin 22.5°
\[\sin(22.5) = \frac{ 45 }{ 2 }\] use ur double angle formula \[\sin(\frac{ 1 }{ 2 }*x) = 0 \pm \sqrt{\frac{ 1-\cos(x) }{ 2 }}\] where x = 45.
Ans: \[\sqrt{\frac{ 2-\sqrt{2} }{ 2 }}\]
there should only be a root on the numerator.
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 \[\frac{ \sqrt{2-\sqrt{2}} }{ 2 }\]?
actually \[\frac{ \sqrt{2-\sqrt{2}} }{ 2 }\] is not an option for answers
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 \[\sqrt{(1-\cos(\pi/4))/2}\] = \[\sqrt{(1-\sqrt{2}/2)/2}\]
the answer simplifies to \[1/2 \sqrt{2-\sqrt{2}}\]