I can't seem to find the error. I need a fresh pair of eyes. I am trying to calculate the values of Cos/Sin/Tan of an angle in C++ without using built-in functions or libraries. These are the only requirements.
This is what I have gotten so far: I have written a function to calculate the exponential values, factorials and the required values.
I keep getting errors and I don't know where they originate from. Some numbers give me exactly the right answers and others are so far off. So could you tell me what I am doing wrong here?
#include <iostream>
#include <cmath>
using namespace std;
double bernoulli_numbers[] = { 1, -1/2.0, 1/6.0, -1/30.0, 5/66.0, -691/2730.0, 7/6.0, -3617/510.0, 43867/798.0, -174611/330.0, 854513/138.0};
int angleToRadian(int angle) {
float rad_angle;
rad_angle = angle * (M_PI / 180);
return rad_angle;
}
int calculatingExponents(int num, int power) {
long double result = 1;
for (int i = 0; i < power ; ++i) {
result *= num;
}
return result;
}
unsigned long long calculatingFactorials(int n) {
unsigned long long factorial = 1;
if ( n < 0 ) {
cout << "Can't compute factorials for negative numbers" << endl;
}
else if ( n < 2 ) {
return 1;
}
else {
for (int i = n; (i >= 2) ; i--) {
factorial = factorial * i;
}
}
return factorial;
}
void calculatingCos(double angle) {
long double numerator;
long double last_term;
unsigned long long denominator;
long double result;
long double final_result = 0;
for (int i = 0; i < 15; ++i) {
numerator = calculatingExponents(-1, i);
denominator = calculatingFactorials(2 * i);
last_term = calculatingExponents(angle, (2 * i));
result = (numerator / denominator) * last_term;
final_result += result;
}
cout << "The Cosine of the angle = " << final_result << endl;
}
void calculatingSin(double angle) {
long double numerator;
long double last_term;
unsigned long long denominator;
long double result;
long double final_result = 0;
for (int i = 0; i < 15; ++i) {
numerator = calculatingExponents(-1, i);
denominator = calculatingFactorials((2 * i) + 1);
last_term = calculatingExponents(angle, ((2 * i) + 1));
result = (numerator / denominator) * last_term;
final_result += result;
}
cout << "The Sine of the angle = " << final_result << endl;
}
void calculatingTan(double angle) {
int bernoulli_index;
long double bernoulli_number;
long double numerator;
long double last_term;
unsigned long long denominator;
long double result;
long double final_result = 0;
for (int i = 0; i < 15; ++i) {
bernoulli_index = (2 * i) + 2;
bernoulli_number = bernoulli_numbers[bernoulli_index];
numerator =
calculatingExponents(-1, i)
*
calculatingExponents(2, (2 * i) + 2)
*
( calculatingExponents(2, (((2 * i) + 2) * 1)) - 1) * bernoulli_number;
denominator = calculatingFactorials((2 * i) + 2);
last_term = calculatingExponents(angle, (2 * i) + 1);
result = (numerator / denominator) * last_term;
final_result += result;
}
cout << "The Tan of the angle = " << final_result << endl;
}
int main() {
int degree_angle;
int x;
cout << "Please input an angle in degrees:" << endl;
cin >> degree_angle;
x = angleToRadian(degree_angle);
calculatingCos(x);
calculatingSin(x);
calculatingTan(x);
}
Some the errors I am getting are:
Input: 180
Output:
The Cosine of the angle = -0.989992
The Sine of the angle = 0.14112
The Tan of the angle = 3.49908e+07
Expected Outputs:
The Cosine of the angle = -1
The Sine of the angle = 0
The Tan of the angle = 0
Input: 60
Output:
The Cosine of the angle = 0.540302
The Sine of the angle = 0.841471
The Tan of the angle = 1705.3
Expected Outputs:
The Cosine of the angle = 0.5
The Sine of the angle = 0.86602540378
The Tan of the angle = 1.73205080757
A lot of parameters and variables are int when they only make sense as doubles.
#include <iostream>
#include <cmath>
using namespace std;
double bernoulli_numbers[] = { 1, -1/2, 1/6, -1/30, 5/66, -691/2730, 7/6, -3617/510, 43867/798, -174611/330, 854513/138};
double angleToRadian(int angle) {
double rad_angle = angle * (M_PI / 180);
return rad_angle;
}
angleToRadian previously returned an int, there are pi radians in a circle so angles under 360 degrees are going to snap to 0, 1, 2 or 3 radians. You need to return a decimal to get a correct conversion.
long double calculatingExponents(double num, int power) {
long double result = 1;
for (int i = 0; i < power ; ++i) {
result *= num;
}
return result;
}
The num parameter in calculatingExponents takes the decimal angle as a result of angleToRadians, so num, result and the return type of calculatingExponents all need to be floating point numbers too.
unsigned long long calculatingFactorials(int n) {
unsigned long long factorial = 1;
if ( n < 0 ) {
cout << "Can't compute factorials for negative numbers" << endl;
}
else if ( n < 2 ) {
return 1;
}
else {
for (int i = n; (i >= 2) ; i--) {
factorial = factorial * i;
}
}
return factorial;
}
If you're using an unsigned long long but returning an int, you're relying on implementation defined behaviour, so have no guarantees of a reasonable answer.
int main() {
int degree_angle = 45;
cout << "Angle in degrees: " << degree_angle << endl;
double x = angleToRadian(degree_angle);
calculatingCos(x);
calculatingSin(x);
calculatingTan(x);
}
Again angleToRadian returns a floating point number, so x needs to be a floating point type.
These modifications seems to correct sine and cosine between -90 and 90 degrees.
I'm not yet sure what mistake is happening in the tangent calculation.