Write codes in C++ or show Mathematic appendum please.

Approximate (f(x) = arcsin(x) on the interval -1/2, 1/2 by an interpolating polynomial of degree 15, P_15(x). Use equally spaced nodes. How many? Show the plot of the original function and the interpolation. Now determine how accurate the approximation is by numerical tests; you want to find maximum error, that is max. of |f(x) - P_15(x)| on the entire interval, discredited to h = 10^-3 Approximate (f(x) = arcsin(x) on the interval -1/2, 1/2 by an interpolating polynomial of degree 15, P_15(x). Use equally spaced nodes. How many? Show the plot of the original function and the interpolation. Now determine how accurate the approximation is by numerical tests; you want to find maximum error, that is max. of |f(x) - P_15(x)| on the entire interval, discredited to h = 10^-3