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

Question

Given: tanh(x) = 1 - 2 e^-2x + 2 e^x^-4x - 2 e^-6x + 2 e^-8x - 2 e^-10x + .... cos(x)= 1 -x^2/(2!) + x^4/(4!) - x^6/(6!) + x^8/(8!) + .... where 0 lessthanorequalto x lessthanorequalto 2 pi Write two functions: 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. Write a program to test the functions by computing F = 5 tanh(ax) + 4 cos(ax) where 0 lessthanorequalto x

Explanation / Answer

#include<iostream>
#include<cmath>

using namespace std;

double fact(double n)
{
   double fact=1;
   for(int i = 1; i <=n; ++i)
{
fact *= (double)i;
}
  
   return fact;
}

double tanh(double a, double x){
   double sum = 0,t=1.00,y=0;
   int i=0;
   x = x*a;
   for(i=0;i<=10;i+=2)
   {
       y = t*2.00*exp(-2.00*x);
       sum+=y;
       t*=-1.00;
   }
   return sum;
}

double cos(double a, double x)
{
   int i;
   double sum=0.00,t=1.00,y=0.00;
   x = x*a;
   for(i=0;i<=8;i+=2)
   {
       sum+=(t*pow(x,(double)i)/fact(i));
       t*=-1.00;
   }
   return sum;
}

int main()
{
   double a,x,res;
  
   cout<<"Enter a: ";
   cin>>a;
   cout<<"Enter x: ";
   cin>>x;
  
   res = 5.00*tanh(a,x) + 4.00*cos(a,x);
  
   cout<<"F = "<<res<<endl;
}

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