Question

The exact value of sin 5pi/12 is?
A) 0.97
B) sqrt(2) ( sqrt(3) + 1) /4
C) sqrt(2) ( sqrt(3) - 1) /4
D) 0.02

Answer 1

you know cos(5pi/6)
any you know 1/2*5pi/6 =5pi/12
so use half angle identity

Answer 2

\[\sin^2(a)=\frac{1}{2}(1-\cos(2a)) \\ \text{ \let } x=2a \text{ which makes } \frac{x}{2}=a \\ \sin^2(\frac{x}{2})=\frac{1}{2}(1-\cos(x)) \\ \text{ your } x=\frac{5\pi}{6} \\ \text{ that is the thing you want to enter } \\ \text{ then you will need to decide which sign to use when solving for } \\ \sin(\frac{1}{2} \cdot \frac{5\pi}{6})\]