Chapter 3.5, Problem 23P

To determine

To calculate:

The equation of the lines which are tangent toe the graph of $f\left(x\right)=\sin x$

$y=\sin x$ at $x=0\text{ and }x=\frac{\pi }{3}$. Obtain the approximation of $\sin \left(\frac{\pi }{6}\right)$ via the help of each tangent line. Explanation if these results are expected to be accurate because these are taken equally away from the point $x=\frac{\pi }{6}$ but on opposite sides. In case the accuracy is distinct then is there any possibility of accounting those differences.