How do you use half angle formula to find $sin 112.5$ ?

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Answer 1 · 2015-05-25T16:52:12

Use trig identity: 2sin^2 a = 1 - cos 2a

$cos 2(112,5) = cos 225 = cos (45 + 180) = -cos 45 = -(sqrt2)/2$

$2sin^2 112.5 = 1 + (sqrt2)/2 = (2 + sqrt2)/2$

$sin^2 112.5 = (2 + sqrt2)/4 = 0.85$

$sin 112.5 = sqrt(2 + sqrt2)/2$

The negative answer is rejected because sin 112.5 is positive.

Check with calculator: sin 112.5 = 0.92 OK

How do you use half angle formula to find sin 112.5sin 112.5?