how do you find the exact value of sin(pi/24)?

Question

the final answer must be fully simplified, no fractions of a fraction

Answer 1

Use the half angle formula and start with what you know, π/6

sin((π/6)/2) = √(1-cos(π/6))/2 = √(1-√3/2)/2 = √(2-√3)/2

So sin(π/12) = √(2-√3)/2

Do the same thing again to get the sin(π/24). To do so requires you to use the half angle formula foe cos(π/12) so you know what to plug into the sin(π/24) equation.