Question

What is the value of `sin((17pi)/12)`?

Answer 1

`sqrt(2 + sqrt3)/2`

Explanation:

Use trig table, unit circle -->
`sin ((17pi)/12) = sin ((5pi)/12 + pi) = - sin ((5pi)/12)`
Find `sin ((5pi)/12)` by using trig identity:
`2sin^2 a = 1 - cos 2a`
`2sin^2 (5pi)/12) = 1 - cos ((5pi)/6) = 1 + sqrt3/2 = (2 + sqrt3)/2`
`sin^2 ((5pi)/12) = (2 + sqrt3)/4`
`sin ((5pi)/12) = +- sqrt(2 + sqrt3)/2`
Take the positive value because `sin ((5pi)/12)` is positive.
Finally:
`sin ((17pi)/12) = - sin ((5pi)/12) = - sqrt(2 + sqrt3)/2`