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

Question

1085 views around the world

You can reuse this answer
Creative Commons License

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#