How do you use the half angle formula for $sin ((5pi)/12)$ ?

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Answer 1 · 2015-05-04T18:49:21

What is $(5pi)/12$ half of?

It is half of its double: $2 xx (5pi)/12 = 2/1*(5pi)/12 =(5pi)/6$

$sin(1/2x) = +-sqrt((1-cosx)/2)$

We know that $(5pi)/12$ is in quadrant I, so it has positive sine,

$sin((5pi)/12) = sin(1/2((5pi)/6)) = sqrt((1-cos((5pi)/6))/2)$

$= sqrt((1-sqrt3/2)/2) = sqrt((2-sqrt3)/4) = sqrt(2-sqrt3)/2$

How do you use the half angle formula for sin ((5pi)/12)sin ((5pi)/12)?