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anonymous
 5 years ago
Find the exact value of cos(22.500000000 degrees), without a calculator, using doubleangle and/or halfangle identities.
anonymous
 5 years ago
Find the exact value of cos(22.500000000 degrees), without a calculator, using doubleangle and/or halfangle identities.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0cos(x/2) = cos^2(x/4)  sin^2(x/2)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so cos^2 (x/4) = (1/2) ( 1+ cos(x/2) )

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and take sqrt of both sides , note that you do get + when you take a sqrt , but we do know that the angle is in the first quadrant and therefore the cos of the angle must be positive

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so cos22.5 = \[\frac{1}{\sqrt{2}} ( 1+ \frac{1}{\sqrt{2}}) = \frac{1}{\sqrt{2}} +\frac{1}{2} = \frac{\sqrt{2} + 1 }{ 2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wait thats wrong , should be

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{1}{\sqrt{2}} \sqrt{ 1 + \frac{1}{\sqrt{2}} }\]
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