How do I find the value of sin(pi/12)?

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Answer 1 · 2015-09-17T20:38:10

$sin(pi/12) = sqrt(2-sqrt(3))/2$

Using the half-angle formula!

While we don't know what $sin(pi/12)$ is, we do know what $sin(pi/6)$ is, since the latter is one of the special angles (30º to be precise).

We know that $sin(x/2) = +-sqrt([1-cos(x)]/2)$ so we know that

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

It's positive because it's on the first quadrant.

$cos(pi/6) = sqrt3/2$ if you'll remember it, so
$1 - cos(pi/6) = 1 - sqrt3/2 = (2 - sqrt(3))/2$

Since it's divided by 2 we have that
$sin(pi/12) = sqrt([2-sqrt(3)]/4)$

We can put that 4 out of the exponent

$sin(pi/12) = sqrt(2-sqrt(3))/2$