User Functions

[sl02ggp]

Finding difficulty creating a user function program:


Given: tanh (x) = 1-2e^(-2x) + 2e^(-4x) - 2e^(-6x) + 2e^(-8x) -2e^(-10x) + ...
cos(x) = 1-x^(2)/(2!) + x^(4)/(4!) - x^(6)/(6!) + x^(8)/(8!) +...

Trying to write two functions as follows:
tanh(ax) where a and x are passed to the function and
cos (ax) where a and x are passed to the function.

The functions must give answers that are accurate at least to six
significant digits.

With this in mind, I'm trying to write a program that tests the functions, by
computing F= 5tanh(ax) +4cos(ax) where 0 less than or equal to x less than or equal to 2*pi
with the values of a and x entered by the user.

*I would probably check the answers with a calculator.

Check the functions with this data:
a
0
2.78
0
1
1.5
3.78

x
0
0
2.78
2.78
2.6
1

F
4
4
4
1.220321454
2.092175112
1.782610497

Have these programs so far:

e^(x)

#include <iostream>
#include <iomanip>
using namespace std;

int main()
{
	int i,j, n;
	
	double ex = 1, factorial, x, xpower = 1;

	cout << "This program will approximate e value using a finite terms \n";
	cout << "in the exponential series.";
	cout << "\nEnter an integer n to specify the number of terms in series: ";
	cin >> n;
	cout << "\nEnter the value x for e to x: ";
	cin >> x;
	
	for (i=0; i < n-1; i++)			//number of terms: n
	{
		factorial = 1;
		for ( j=0; j< i+1; j++)
			factorial = factorial * (j+1);	//calculate 1 * 2 * 3* .. * i
		xpower = xpower * x;
		ex = ex + xpower / factorial;
	}
	cout << setprecision(20);
	cout << "For 10 terms, the e to x value = " << ex << endl;
}

sin(x)

#include <iostream>
#include <iomanip>
#define PI 3.14159265358979
using namespace std;
int main()
{
	int i,j, n;
	
	double x, xsmall, temp, sin_x, x_power, factorial;

	cout << "This program will approximate sin(x) value using a finite terms \n";
	cout << "in the exponential series.";
	cout << "\nEnter an integer n to specify the number of terms in series: ";
	cin >> n;
	cout << "\nEnter the value of x: ";
	cin >> x;
	
//Transform x to less than 2 PI; i.e. xsmall is less than 2 PI
	temp = x / (2 * PI);
	xsmall = ( temp - int (temp)) * 2 * PI;

//Another way to transform x to less than 2 PI; i.e. xsmall is less than 2 PI
//	xsmall = x;
//  while ( xsmall >= 2 * PI)
//		xsmall = xsmall - (2 * PI);

	sin_x = xsmall;
	
	for (i=0; i < n-1; i++)			//number of terms: n
	{
		factorial = 1;
		x_power = 1;
		for ( j=0; j< 2*i+3; j++)
		{
			factorial = factorial * (j+1);	//calculate  1*2*3*(j+1)!
			x_power = x_power * xsmall;			//calculate x_power exp(k)
		}
		if ( i%2 == 0)
			sin_x = sin_x - x_power / factorial;  //for i even
		else
			sin_x = sin_x + x_power / factorial;  //for i odd
	}
	cout << setprecision(10);
	cout << "For " << n << " terms, the sin(" << x <<") value = " 
		 << sin_x << endl;
}

cos(x):

#include <iostream>
#include <iomanip>
#define PI  3.14159265358979
using namespace std;

int main()
{
	int i,j, n;
	
	double x, xsmall, temp, cos_x, x_power, factorial;

	cout << "This program will approximate cos(x) value using a finite terms \n";
	cout << "in the exponential series.";
	cout << "\nEnter an integer n to specify the number of terms in series: ";
	cin >> n;
	cout << "\nEnter the value of x: ";
	cin >> x;

//Transform x to less than 2 PI; i.e. xsmall is less than 2 PI
	temp = x / (2 * PI);
	xsmall = ( temp - int (temp)) * 2 * PI;

//Another way to transform x to less than 2 PI; i.e. xsmall is less than 2 PI
//	xsmall = x;
//  while ( xsmall >= 2 * PI)
//		xsmall = xsmall - (2 * PI);
	
	cos_x = 1;
	
	for (i=0; i < n-1; i++)			//number of terms: n
	{
		factorial = 1;
		x_power = 1;
		for ( j=0; j< 2*i+2; j++)
		{
			factorial = factorial * (j+1);	//calculate  1*2*3*(j+1)!
			x_power = x_power * xsmall;			//calculate x_power exp(k)
		}
		if ( i%2 == 0)
			cos_x = cos_x - x_power / factorial;  //for i even
		else
			cos_x = cos_x + x_power / factorial;  //for i odd
	}
	cout << setprecision(10);
	cout << "For " << n << " terms, the cos(" << x <<") value = " 
		 << cos_x << endl;
}

[sl02ggp]

can anyone help me with writing this code:
Trying to write a larger program incorporating each of the above programs as functions. Also using each to generate a result and then check the result with another new function which uses the actual functions provided by the math..h header (for which we use this in C++ #include <cmath> )

Also like I said before:

I'm trying to write a program that tests the functions, by
computing F= 5tanh(ax) +4cos(ax) where 0 less than or equal to x less than or equal to 2*pi
with the values of a and x entered by the user.