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half angle identity!!!!!!!!!!!!!

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Use half angle identity to find cos 22 1/2 deg

asked Jun 26, 2013 in TRIGONOMETRY by harvy0496 Apprentice

1 Answer

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Since 22.5 is half of 45, we can use the half-angle identity for cosine:

That is cos(22.50) = cos(450/2)

Let us take 450 as A => cos(A/2) = +/- √((1+cosA)/2)

 

+/-sqrt[(1+cos(45*))/2] = +/-sqrt[(1+sqrt[2]/2)/2] = +/-sqrt[((2+sqrt[2])/2)/(2/1)] = +/-sqrt[2+sqrt[2]]/2

Since 22.5° is in the first quadrant, then the cosine value is positive, hence we can take the positive root.

i.e, +√(2 +√2)/2.

answered Jun 26, 2013 by joly Scholar

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