Find the linearization of $\displaystyle {y}={\sin{{x}}}$ at $\displaystyle {x}=\frac{\pi}{{6}}$, and use your result to approximate $\displaystyle {\sin{{\left(\frac{{{9}\pi}}{{42}}\right)}}}$. Enter exact values only and don't leave trigonometric functions unevaluated.

(a) What is $\displaystyle {\left.{d}{x}\right.}$?  

     

(b) Using your linearization, approximate $\displaystyle {\sin{{\left(\frac{{{9}\pi}}{{42}}\right)}}}$.  

       $\displaystyle {\sin{{\left(\frac{{{9}\pi}}{{42}}\right)}}}\approx$