Task:

Calculate the value of the function y, representing function in Taylor series. The argument varies from -2 to 2 in increments of 0.5. Identify the error.

Block scheme of the solution:

C++ implementation:

#include<iostream> #include<math.h> #include<iomanip> using namespace std; double error; double mysin(double x)//my sin function { double item = x, sum = x; for (int i = 3;; i += 2)//endless cycle { item *= -1 * (x*x) / ((i - 1)*i);//Taylor series if (fabs(item) <= error) break;//exit condition sum += item; } return sum; } void main() { cout << "if 0<x<1 y=sinx-sin(x/2)\nif -2<=x<=0 y=sinx^3-sin(x+0.125)\n"; cout << "enter error="; cin >> error;//input error double y, y2, error; const double min = -2, max = 2, step = 0.5; cout << setw(10) << "x" << setw(20) << "my sin" << setw(20) << "st. sin" << setw(20) << "error" << endl << endl;//output string-header for (double x = min; x <= max; x += step)//cycle: x from -2 to 2 with step 0.5 { if (x>0 && x<1) { y = mysin(x) - mysin(x / 2);//my sin calculating y2 = sin(x) - sin(x / 2);//standart sin calculating error = fabs(y - y2);//compareing/calculating error cout << setw(10) << x << setw(20) << y << setw(20) << y2 << setw(20) << error << endl;//output result } else if (x >= -2 && x <= 0) { y = pow(mysin(x), 3) - mysin(x + 0.125);//my sin calculating y2 = pow(sin(x), 3) - sin(x + 0.125);//standart sin calculating error = fabs(y - y2);//compareing/calculating error cout << setw(10) << x << setw(20) << y << setw(20) << y2 << setw(20) << error << endl;//output result } else//if x doen't fit the condition cout << setw(10) << x << setw(20) << "undefined" << setw(20) << "undefined" << endl; } system("pause");//pause console }

Screenshot of the working program:

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