Calculating the taylor series of sinx in C [duplicate] - c

Question

Task: According to the Taylor Series of sin(x) calculate with using a double function named mysin pass it to a double variable. Take a x value from user and use the mysin function to calculate sin(x).
Problem is program gives me wrong value of sin(x). I have been trying to solve that issue about 4 hours but couldn't find it. Is it because of sin(x) function or have I missed something in my code?
My Code:
#include <stdio.h>
double mysin(double x)
{
double value = x;
double sum = x;
int neg_pos = 1;
int fac = 1;
int counter = 0;
while(1)
{
neg_pos *= -1;
fac += 2;
value = value/(fac*(fac-1));
value = value*x*x*neg_pos;
sum += value;
//printf("Hello");
counter++;
if (counter == 100) break;
}
return sum;
}
int main()
{
double number;
scanf("%lf",&number);
printf("%g",mysin(number));
//printf("%g",number);
}

Answer 1

The problem is that you're multiplying by neg_pos each step, which toggles between +1 and -1. That means the terms change sign only half the time, whereas they should change sign each time.
The fix is to just multiply by -1 each time rather than neg_pos.
Here's a working, slightly-simplified form of your program that calculates sin for a range of numbers from 0 to 3, showing the stdlib calculation to compare.
#include <math.h>
#include <stdio.h>
double mysin(double x) {
double value = x;
double sum = x;
int fac = 1;
for (int counter = 0; counter < 100; counter++) {
fac += 2;
value = -value*x*x/fac/(fac-1);
sum += value;
}
return sum;
}
int main() {
for (double x = 0.0; x < 3.0; x += 0.1) {
printf("%g: %g %g\n", x, mysin(x), sin(x));
}
}
You can also avoid the separate fac and counter variables, perhaps like this:
double mysin(double x) {
double term=x, sum=x;
for (int f = 0; f < 100; f++) {
term = -term*x*x/(2*f+2)/(2*f+3);
sum += term;
}
return sum;
}

Answer 2

From what I'm understanding you are not calculating the power correctly
Firtsly use this:
#include <math.h>
Then create a factorial function:
int factorial(int x){
int result = 1;
for(int i = 1; i < x; i++){
result += result * i;
}
return result;
}
And finally:
while(1)
{
neg_pos *= -1;
fac += 2;
power = pow(x,fac);
fac = factorial(fac);
sum += power/fac;
//printf("Hello");
counter++;
if (counter == 100) break;
}