Question

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

Answer 1

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

Explanation:

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`