Example of Assignment: Cycles with Conditional Statement

Task:

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

\left\{\begin{matrix}sin(x) - sin(x/2), \ \ \ \ \ \ \ \ \ \ \ \ 0 < x < 1, \\sin(x)^3 - sin(x + 0.125), \ \ -2 \leqslant x \leqslant 0. \end{matrix}\right.

Block scheme of the solution:

sample-cycles-with-conditional-statement-1

sample-cycles-with-conditional-statement-2

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:

sample-cycles-with-conditional-statement32

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