Tutorial - Sine Taylor

Tutorial - Programming sin(x) (In Class Activity)

Preparation

1) PPT Download: Download Supplementary PPT

2) You must follow the Tutorial: Tutorial: NP Library Header Files

3) You must do: Assignment 0

Problem 1

Introduction

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 Assignment 0

Procedure

• Create a new empty project in Visual Studio Community

  • Name the project as: TU_TaylorSeries

• It should be saved under \tutorial directory

  • i.e.: C:\Users\yourID\source\repos\NP\tutorial\TU_TaylorSeries

• Create a new C/C++ source file for main()

  • Name the source file as TU_taylorSeries_exercise.cpp

• Copy the source code from

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

image

Pseudocode for Programming Sine with Taylor series

image

Pseudocode for Programming power()

image

Video for Problem 1

See here for the TA Tutorial Video

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Problem 2

Introduction

Define your sinTaylor(x) in the NP library header file

Procedure

• Create a new empty project in Visual Studio Community

  • Name the project as: TU_TaylorSeries_Part2

• It should be saved under \tutorial directory

  • i.e.: C:\Users\yourID\source\repos\NP\tutorial\TU_TaylorSeries_Part2

• Create a new C/C++ source file for main()

  • Name the source file 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;
}

(Library File Preparation)

• Under the directory of \include, prepare header files

  • Files: myNP_tutorial.cpp and myNP_tutorial.h.

  • C:\Users\yourID\source\repos\NP\include

  • You can download source files here

  • This is the same header file as in Tutorial: NP Library Header Files Step 3. Create library header files

These files should be saved in “ \include\” folder.

image

(Library File Update)

• Update the header files

  • Your sinTaylor(rad) of Problem 1 should be declared and defined in the header file.

  • See below as example

myNP_tutorial.h

/*----------------------------------------------------------------\
@ 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

myNP_tutorial.c

• Run and check the answer

Video for Problem 2

See here for the TA Tutorial Video

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Exercise

1. Create double cosTaylor(double rad)

2. Create double expTaylor(double x)

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After you have completed all the exercises, you can check sample solutions here

Exercise solutions

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