Question

Using half angle identities, find an EXACT expression for sin(7π/12).

Answer 1

±
`(1+√(3) )/(2√(2) )`

Explanation:

We can rewrite
`sin((7\pi )/(12) )` as
`sin((7\pi )/(6) ((1)/(2) ))`. The half-angle identity for sin tells us that
`sin((x)/(2) ) = \sqrt{(1 - cos(x))/(2) }` (plus or minus). Now, we can plug in
`(7\pi )/(6)` for x. When we do that, we get
`\sqrt{(1 - (-(√(3))/(2)) )/(2) }` = ±
`(1+√(3) )/(2√(2) )`.

Hope this helped! :)