Compute tan(x) to be infinity in C++ - c++

Question

#include <iostream>
#include <math.h>
#include <cstdlib>
using namespace std;
double cosin_value( double value );
double sin_value( double value );
double big_degree( double value );
double big_radian( double value );
double x;
double value;
double degree;
double radian;
const double PI = 3.14159;
char choice;
char yes;
int main()
{
cout << "Please enter an angle value => ";
cin >> value;
cout << "Is the angle in Degree or Radian?" << endl;
cout << "\t" << "Type D if it is in Degree" << endl;
cout << "\t" << "Type R if it is in Radian" << endl;
cout << "Your response => ";
cin >> choice; //degree or radian?
cout.setf(ios::fixed);
cout.setf(ios::showpoint);
cout.precision(10);
if (choice == 'D' || choice == 'd')
{
big_degree (value);
cout << " " << "sin(x) = " << "\t" << sin_value(degree) << endl;
cout << " " << "cos(x) = " << "\t" << cosin_value(degree) << endl;
cout << " " << "tan(x) = " << "\t" << sin_value(degree) / cosin_value(degree) << endl;
}
else if (choice == 'R' || choice == 'r')
{
big_radian (value);
cout << " " << "sin(x) = " << "\t" << sin_value(radian) << endl;
cout << " " << "cos(x) = " << "\t" << cosin_value(radian) << endl;
cout << " " << "tan(x) = " << "\t" << sin_value(radian) / cosin_value(radian) << endl;
}
return 0;
}
// Sine,cosine functions
// angle -360<value<360
double sin_value( double value )
{
int count=1;
double sine, num, dem, sign, term;
sine = 0;
sign = 1;
num = value;
dem = count;
while ( count <= 20 )
{
term = ( num / dem );
sine = sine + term * sign;
num = num * value * value;
count = count + 2;
dem = dem * count * ( count - 1 );
sign = -sign;
}
return (sine);
}
double cosin_value( double value )
{
int count = 0;
double cosine, num, dem, sign, term;
cosine = 0;
sign = 1;
num = 1;
dem = 1;
while ( count <= 20 )
{
term = ( num / dem );
cosine = cosine + term * sign;
num = num * value * value;
count = count + 2;
dem = dem * count * ( count - 1 );
sign = -sign;
}
return (cosine);
}
double big_degree( double value )
{
int result;
const int angle = 360;
if (value >= 360 || value <= -360)
{
result = value / angle;
degree = ( value - ( result * angle ) ) * PI / 180;
}
else
{
degree = ( value * PI ) / 180;
}
return (degree);
}
double big_radian( double value )
{
int result;
if (value >= 2 * PI || value <= -2 * PI)
{
result = value / ( 2 * PI );
radian = ( value - ( result* 2 * PI ) );
}
else
{
radian = value;
}
return (radian);
}
I have few problems here:
How can the program shows tan(x) is infinity when I input a value 90 degree or 1.5708 radian? When I input 90 degree, it gave me an output of 0.0000013268 instead of 0 for cos(x).
I tried to put in this command in my cosin function where If cos(x)<0.00001, set it to zero, it worked for 90 degree but for other values like 2.3145 radian, cos(x) value is 0 instead of -0.677013.
I appreciate your guides!

Answer 1

Use epsilon value just like you mentioned in question #2.
Use an absolute value of cos(x) like abs(cos(x)) in your if statement. .
You can also represent infinity with double or float. Check this link.
http://www.gnu.org/software/libc/manual/html_node/Infinity-and-NaN.html
More importantly, you might want to read this article called "What Every Computer Scientist Should Know About Floating-Point Arithmetic"
http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html
You will notice that each step of your floating point operations will accumulate errors in calculation.