series using program - c

Question

I'm trying to implement my own sin(x) function via maclaurin series using C program,
this is what I have so far, I worked everything on paper first then I tried to implement it it in a code
#include<stdio.h>
#define PI 3.141592653589793238462643383
int main()
{
int x,nOfterms,term=1,i,j;
double numerator,sum=0.0,radius;
long int denominator;
printf("\n\t\tINPUT:");
printf("\n\t\t------");
printf("\n\t\tEnter the value for x in degrees: ");
scanf("%d",&x);
printf("\n\t\tEnter the value for number of terms: ");
scanf("%d",&nOfterms);
printf("\n\t\tOUTPUT:");
printf("\n\t\t-------");
radius=x*(PI/180.0);
printf("\n\t\tThe radius value for the given x value is: %lf",radius);
for(i=1;i<=nOfterms;i+=2)
{
numerator=1.0;
denominator=1;
for(j=1;j<=i;j++)
{
numerator=numerator*radius;
denominator=denominator*j;
}
sum=(sum+numerator)/(denominator*term);
term=term*-1;
}
printf("\n\t\tThe value for sin %d is: %lf",x,sum);
printf("\n\n\n");
return 0;
}
I can't use the math.h at all in my code or so does the professor say,
My output is all zeros which is not right obviously, also I would appreciate if anyone could help me with this, also if anyone can offer a way where I can see each iteration for each number of term of the series on the screen before I arrive at the answer, tried to place the last printf in the for loop but I'll end up with weird symbols and numbers.

Answer 1

The problem in in the implementation of the Mac Laurin series. The line
sum=(sum+numerator)/(denominator*term);
is wrong. It should be simply :
sum += numerator/denominator*term;
Remaining is fine. I tried it and found sin(30) = 0.5, sin(60) = 0.866 and even sin(90) ~ 1.
But you algorythm is not very efficient since for each term you start back from 1/1 when the first elements of in / i! have already been computed on previous term.
You could change your loops to :
numerator=1.0;
denominator=1;
j = 1;
for(i=1;i<=nOfterms;i+=1)
{
numerator=numerator*radius;
denominator=denominator*j++;
sum += numerator/denominator*term;
term=term*-1;
numerator=numerator*radius;
denominator=denominator*j++;
}
Tested and give same (correct) results.

Answer 2

Here are some problems with your code to help you along:
You want to increment i by 1, not 2 as you count the number of terms.
For each term, you want only the odd powers of x, so it's j you need to increment by 2 (change the upper limit and denominator factorial calculation appropriately)
This line is wrong: sum=(sum+numerator)/(denominator*term); and should presumably be sum=sum+numerator/(denominator*term);
Hope that helps with your assignment.

Answer 3

Your inner for loop is not correct. Manually trace through it for a few values of i:
1: numerator=radius, denominator=1 (correct)
2: numerator=radius, denominator=1 (incorrect)
3: numerator=radius*radius, denominator=3 (incorrect)
Correct inner loop should be:
for (j = 1; j < i*2; ++j)
{
numerator = numerator * radius;
denominator = denominator * j;
}