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JeffreyFloria236 JeffreyFloria236
  • 15-07-2014
  • Mathematics
Answered

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

sin 22.5degrees

show your work. thanks!

Verified Answer :

luana
luana luana
  • 07-08-2014

\(sin( \frac{ \alpha }{2})=\sqrt{ \frac{1-cos\alpha}{2} }\\\alpha=45^\circ\\ sin(22,5)=\sqrt{ \frac{1-cos45}{2} }\\ sin(22,5)=\sqrt{ \frac{1-\frac{\sqrt2}{2}}{2} }\\ sin(22,5)=\sqrt{ \frac{2-\sqrt2}{2}*\frac{1}{2} }\\sin(22,5)=\sqrt{ \frac{2-\sqrt2}{4} }\)

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