C Program to Find the Value of sin(x) Using Series

This C program computes the value of sin(x) by summing its Taylor series up to a given accuracy, then compares the result with the built-in sin() library function. It’s a classic exercise in loops, floating-point math, and how a computer approximates trigonometric functions.

The Sine Series

The Taylor series for sine (with x in radians) is:

sin(x) = x - x³/3! + x⁵/5! - x⁷/7! + ...

Each term comes from the previous one by multiplying by -x² / (2n(2n+1)), so there’s no need to compute factorials or powers directly — we just keep adding terms until the sum is accurate enough.

The Program

#include <stdio.h>
#include <math.h>

#define PI 3.14159265358979323846

int main(void)
{
    int n, deg;
    double acc, term, x, sinx, sinval;

    printf("Enter the value of x (in degrees) : ");
    scanf("%d", &deg);

    printf("Enter the accuracy for the result : ");
    scanf("%lf", &acc);

    x = deg * (PI / 180.0);   /* convert degrees to radians */
    sinval = sin(x);          /* reference value from the library */

    term = x;                 /* first term of the series */
    sinx = term;
    n = 1;

    do {
        term = -term * x * x / (2.0 * n * (2.0 * n + 1.0));
        sinx += term;
        n++;
    } while (fabs(sinval - sinx) >= acc);

    printf("Sum of the sine series         = %lf\n", sinx);
    printf("Using library function sin(%d) = %lf\n", deg, sinval);
    return 0;
}

How the Program Works

The angle is read in degrees and converted to radians, because C’s sin() works in radians.
term starts at x (the first series term). Each pass multiplies it by -x² / (2n(2n+1)) to get the next term and adds it to sinx.
The loop stops once the running sum is within acc of the library’s sin(x), giving you control over the accuracy.
We use double and a full-precision π constant for accuracy, improving on the old 3.142 value.

Compiling (link the math library)

On Linux and macOS, link the math library with -lm:

gcc sinx.c -o sinx -lm

Sample Output

Enter the value of x (in degrees) : 30
Enter the accuracy for the result : 0.00001
Sum of the sine series         = 0.500000
Using library function sin(30) = 0.500000

For a clear explanation of C’s numeric types and the math library, The C Programming Language by Kernighan and Ritchie is the classic reference — find it on Amazon.

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C program to find the value of sin(x)