Chapter 4, Problem 19P

To calculate a planet's space coordinates, we have to solve the Function

$f\left(x\right)=x-1-0.5\sin x$

Let the base point be $a=x_i=\pi /2$ on the interval $\left[0,\pi \right]$. Determine the highest-order Taylor series expansion resulting in a maximum error of 0.015 on the specified interval. The error is equal to the absolute value of the difference between the given function and the specific Taylor series expansion. (Hint: Solve graphically.)