anonymous
  • anonymous
Find the exact value by using a half-angle identity. sin 22.5°
Mathematics
chestercat
  • chestercat
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abb0t
  • 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.
abb0t
  • abb0t
Ans: \[\sqrt{\frac{ 2-\sqrt{2} }{ 2 }}\]
abb0t
  • abb0t
there should only be a root on the numerator.

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anonymous
  • 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 \[\frac{ \sqrt{2-\sqrt{2}} }{ 2 }\]?
anonymous
  • anonymous
actually \[\frac{ \sqrt{2-\sqrt{2}} }{ 2 }\] is not an option for answers
anonymous
  • 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 \[\sqrt{(1-\cos(\pi/4))/2}\] = \[\sqrt{(1-\sqrt{2}/2)/2}\]
anonymous
  • anonymous
the answer simplifies to \[1/2 \sqrt{2-\sqrt{2}}\]

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