Question #8e1d5

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Question #8e1d5

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Answer 1 · 2016-07-27T12:52:01

$\sqrt{(\frac{1}{2}) (1 - (\frac{\sqrt{3} + 1}{2 \sqrt{2}}))}$ $sqrt((1/2)(1-((sqrt 3 + 1)/(2 sqrt 2))))$

$= 0.1305$ $=0.1305$ , nearly

Explanation:

Angle is in degree unit.

$sin (\frac{15}{2})$ $sin(15/2)$

$= \sqrt{\frac{1 - cos 15}{2}}$ $=sqrt((1-cos 15)/2)$

$= \sqrt{(\frac{1}{2}) (1 - cos (45 - 30))}$ $=sqrt((1/2)(1-cos(45-30))$

$= \sqrt{(\frac{1}{2}) (1 - (cos 45 cos 30 + sin 45 sin 30))}$ $=sqrt((1/2)(1-(cos 45 cos 30+sin 45 sin 30))$

$= \sqrt{(\frac{1}{2}) (1 - ((\frac{1}{\sqrt{2}}) (\frac{\sqrt{3}}{2}) + (\frac{1}{\sqrt{2}}) (\frac{1}{2})))}$ $=sqrt((1/2)(1-((1/sqrt 2)(sqrt 3/2)+(1/sqrt 2)(1/2)))$

$= \sqrt{(\frac{1}{2}) (1 - (\frac{\sqrt{3} + 1}{2 \sqrt{2}}))}$ $=sqrt((1/2)(1-((sqrt 3 + 1)/(2 sqrt 2))))$

$0.1305$ $0.1305$ , nearly

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Question #8e1d5

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