#include <iostream>
#include <cmath>
#include <iomanip>

using namespace std;

const double pi = atan(1.0)*4.0;

double degreesToRadians(double angleDegrees);
double factorial(int number);
double mySine(double angleRadians);
double myCosine(double angleRadians);
double mySec(double angleRadians);
double myCsc(double angleRadians);
double myCot(double angleRadians);
double myTan(double angleRadians);

int main(){

	cout << endl << endl;
	cout << "Welcome to 'taylor series'!" << endl << endl;
	cout << "Press enter to continue..." << endl << endl;

	cout << setw(23) << "System" << setw(16) << "System" << setw(16) << "System" << endl;

	cout << "Degrees" << setw(8) << "Radians" << setw(8) << "Sin" << setw(8) << "Sin" << setw(8) << "Cos" << setw(8) << "Cos"
		 << setw(8) << "Tan" << setw(8) << "Tan" << setw(8) << "Cotan" << setw(8) << "Secan" << setw(8) << "Cosec" << endl;

	for(double angleDegrees = 0; angleDegrees <= 360; angleDegrees += 15){

		double angleRadians = degreesToRadians(angleDegrees);

		cout << setprecision(4) << fixed << angleDegrees << setw(8) << angleRadians << setw(8) << sin(angleRadians)
		 	 << setw(8) << mySine(angleRadians) << setw(8) << cos(angleRadians) << setw(8) << myCosine(angleRadians) << setw(8)
		 	 << tan(angleRadians) << setw(8) << myTan(angleRadians) << setw(8)
		 	 << setw(8) << myCot(angleRadians) << setw(8)
		 	 << mySec(angleRadians) << setw(8) << myCsc(angleRadians);
	}

	return 0;
}double degreesToRadians(double angleDegrees){
	double angleRadians = (pi/180.0)*angleDegrees;
	return angleRadians;

}double factorial(int number){

	double sum = 1;

	for(int count = 1; count <= number ; count++){
		sum = count*sum;
	}
	return sum;

}

double mySine(double angleRadians){

	double sum = 0, oldsum = 0, diff = 1;
	int alt = 1, i = 1;

	while(diff >= 0.00001){

		sum = sum + alt * pow(angleRadians,i)/factorial(i);

		diff = abs(sum - oldsum);
		oldsum = sum;

		alt = alt * -1;
		i = i + 2;

	}
	return sum;
}

double myCosine(double angleRadians){

	double sum = 0, oldsum = 0, diff = 1;
	int alt = 1, i = 0;

	while(diff >= 0.00001){

		sum = sum + alt * pow(angleRadians,i)/factorial(i);

		diff = abs(sum - oldsum);
		oldsum = sum;

		alt = alt * -1;
		i = i + 2;

	}
	return sum;
}

double myCot(double angleRadians){

	double sum = 0;

	myCosine(angleRadians)/mySine(angleRadians);

	return sum;

}

double myCsc(double angleRadians){

	double sum = 0;

	1/mySine(angleRadians);

	return sum;

}

double mySec(double angleRadians){

	double sum = 0;

	1/myCosine(angleRadians);

	return sum;

}

double myTan(double angleRadians){

	double sum = 0;

	myCos(angleRadians)/mySine(angleRadians);

	return sum;

}