Use an addition or subtraction formula to find the exact value of $\displaystyle {\sin{{\left({\frac{{{19}}}{{{12}}}}\pi\right)}}}=-{\frac{{\sqrt{{{A}}}{\left(\sqrt{{{B}}}+{1}\right)}}}{{{4}}}}$.
$\displaystyle {A}=$ Preview Question 6 Part 1 of 2   ;
$\displaystyle {B}=$ Preview Question 6 Part 2 of 2   .