a) Create sinTaylor(x) that returns the output of sine x, where x is in [rad].
b) Create sindTaylor(x) that returns the output of sine x, where x in in [deg].
You must use your own function of power() and factorial() from
Procedure
Create a new project “ TU_TaylorSeries” with Visual Studio
Create the new source file and name it as “TU_taylorSeries_exercise.cpp”
Copy the source code
C_taylorSeries_exercise.cpp
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define PI 3.14159265358979323846264338327950288419716939937510582
double factorial(int _x);
double power(double _x, int N);
double sinTaylor(double _x);
double sindTaylor(double _x);
int main(int argc, char* argv[])
{
double xdeg = 60;
double x = PI / 3;
double sinN = 0;
double sinDeg = 0;
/*===== Select the function to call =====*/
sinN = sinTaylor(x); // in [rad]
printf("\n\n");
printf("=======================================\n");
printf(" sin( %f[rad] ) Calculation \n", x);
printf("=======================================\n");
printf(" - My result = %3.12f \n", sinN);
printf(" - Math.h result = %3.12f \n", sin(x));
printf(" - absolute err. = %3.12f \n", sinN - sin(x));
printf("=======================================\n");
sinDeg = sindTaylor(xdeg); // in [deg]
printf("\n\n");
printf("=======================================\n");
printf(" sin( %f[deg] ) Calculation \n", xdeg);
printf("=======================================\n");
printf(" - My result = %3.12f \n", sinDeg);
printf("=======================================\n");
system("pause");
return 0;
}
// factorial function
double factorial(int N)
{
int y = 1;
for (int k = 2; k <= N; k++)
y = y * k;
return y;
}
// power function
double power(double _x, int N)
{
double y = 1;
for (int k = 1; k <= N; k++)
y = y * _x;
return y;
}
// Taylor series approximation for sin(x) (input unit: [rad])
double sinTaylor(double _x)
{
int N_max = 10;
double sinN = 0;
for (int k = 0; k < N_max; k++)
// [TODO] add your algorithm here
return sinN;
}
// Taylor series approximation for sin(x) (input unit: [deg])
double sindTaylor(double _x)
{
double sinDeg=0;
// [TODO] add your algorithm here
return sinDeg;
}
Fill in the definition of sinTaylor(rad) in the main source.
Compare your answer and calculate the absolute error
sin(π/3)= 0.86602540378
Create sindTaylor(deg) for degree unit input and output.
Hint: re-use sinTaylor(rad) definition
TIP
Approximation of Sine with Taylor series
Pseudocode for Programming Sine with Taylor series
Pseudocode for Programming power()
Part 2
Define your sinTaylor(x) in the NP library header file
Procedure
Create a new project “ TU_TaylorSeries_Part2” with Visual Studio
Create the new source file and name it as “TU_taylorSeries_exercise_part2.cpp”
Copy the source code
C_taylorSeries_exercise_part2.cpp
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
//#define PI 3.14159265358979323846264338327950288419716939937510582
#include "../../include/myNP_tutorial.h"
int main(int argc, char* argv[])
{
double xdeg = 60;
double x = PI / 3;
double sinN = 0;
double sinDeg = 0;
/*===== Select the function to call =====*/
sinN = sinTaylor(x); // in [rad]
printf("\n\n");
printf("=======================================\n");
printf(" sin( %f[rad] ) Calculation \n", x);
printf("=======================================\n");
printf(" - My result = %3.12f \n", sinN);
printf(" - Math.h result = %3.12f \n", sin(x));
printf(" - absolute err. = %3.12f \n", sinN - sin(x));
printf("=======================================\n");
sinDeg = sindTaylor(xdeg); // in [deg]
printf("\n\n");
printf("=======================================\n");
printf(" sin( %f[deg] ) Calculation \n", xdeg);
printf("=======================================\n");
printf(" - My result = %3.12f \n", sinDeg);
printf("=======================================\n");
system("pause");
return 0;
}
Update the existing library header files named as myNP_tutorial.h and myNP_tutorial.c
These files should be saved in “ \include\” folder.
Your sinTaylor(rad) of Exercise 1 should be declared and defined in the header file.
/*----------------------------------------------------------------\
@ Numerical Methods by Young-Keun Kim - Handong Global University
Author : SSS Lab
Created : 05-03-2021
Modified : 05-03-2021
Language/ver : C in MSVS2019
Description : myNP_tutorial.h
/----------------------------------------------------------------*/
#ifndef _MY_NM_H // use either (#pragma once) or (#ifndef ...#endif)
#define _MY_NM_H
#define PI 3.14159265358979323846264338327950288419716939937510582
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
// Factorial function
extern double factorial(double _x);
extern double power(double _x, int N);
// Taylor series approximation for sin(x) using pre-defined functions (input unit: [rad])
extern double sinTaylor(double _x);
// Taylor series approximation for sin(x) using pre-defined functions (input unit: [deg])
extern double sindTaylor(double _x);
#endif
/*----------------------------------------------------------------\
@ C-Tutorial by Young-Keun Kim - Handong Global University
Author : SSS LAB
Created : 05-03-2021
Modified : 08-19-2022
Language/ver : C++ in MSVS2022
Description : myNP_tutorial.c
/----------------------------------------------------------------*/
#include "myNP_tutorial.h"
// factorial function
double factorial(int N)
{
// [TODO] add your algorithm here
return 0;
}
// power function
double power(double _x, int N)
{
// [TODO] add your algorithm here
return 0;
}
// Taylor series approximation for sin(x) using pre-defined functions (input unit: [rad])
double sinTaylor(double _x)
{
int N_max = 10;
double sinN = 0;
//for (int k = 0; k < N_max; k++)
// [TODO] add your algorithm here
return sinN;
}
// Taylor series approximation for sin(x) using pre-defined functions (input unit: [deg])
double sindTaylor(double _x)
{
double sinDeg = 0;
// [TODO] add your algorithm here
return sinDeg;
}
Run and check the answer
Extra Work
Create double cosTaylor(double rad)
Create double expTaylor(double x)
After you have completed all the exercises, you can check sample solutions here
