[size=100][br][math]f\left(z\right)=sin\left(z\right)[br][/math][br][math]g(z)=z-\frac{z^3}{6}[br][/math][br][br]The function [math]g\left(z\right)[/math] is used to approximate [math]f\left(z\right)[/math] for [math]z=a+0.4i[/math] where [math]a>0[/math].[br][br]Construct a spreadsheet that will calculate the error in the real part of this approximation for different values of a. State the formulae you have used in your spreadsheet.[br][br]Use your spreadsheet to find, correct to 1 decimal place, the minimum positive value [br]of a such that the real part of [math]g\left(z\right)[/math] exceeds the real part of [math]f\left(z\right)[/math] by more than 0.001.[/size]