User Functions

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)

Code:

#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)

Code:

#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):

Code:

#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; }