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

Question

24368 views around the world

You can reuse this answer
Creative Commons License

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