C Math sin() Function

What You’ll Learn

The sin() function computes the sine of an angle. In C, the angle must be in radians. The result is always between −1 and 1—the building block for waves, oscillations, and circular motion.

Definition and Usage

Sine relates an angle to a ratio on a right triangle: opposite ÷ hypotenuse. On the unit circle (radius 1), sin(θ) is the y-coordinate at angle θ.

In C, sin(x) expects x in radians. One full turn is 2π radians (360°). A quarter turn is π/2 radians (90°).

📝 Syntax

Standard C declaration:

double sin(double x);

Related variants

float sinf(float x);           /* <math.h> */
long double sinl(long double x); /* <math.h> */

Parameters

• x — angle in radians.

Return Value

• Sine of x, in the range [−1, 1].
• sin(0) returns 0.0; sin(M_PI / 2) returns 1.0.
• sin(M_PI) returns 0.0 (within floating-point tolerance).

Headers and linking

• #include <math.h>
• Compile: gcc sin.c -std=c11 -o sin -lm
• On MSVC, define _USE_MATH_DEFINES before <math.h> for M_PI.

Examples Gallery

Compile every example with gcc file.c -std=c11 -o out -lm. All angles below are converted to radians before calling sin().

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

int main(void) {
    double degrees = 60.0;
    double radians = degrees * M_PI / 180.0;
    double result = sin(radians);

    printf("Sine of %.1f degrees (%.3f radians): %.3f\n",
           degrees, radians, result);

    return 0;
}

Sine of 60.0 degrees (1.047 radians): 0.866

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

int main(void) {
    printf("sin(0)      = %.1f  (0 degrees)\n", sin(0.0));
    printf("sin(M_PI/2) = %.1f  (90 degrees)\n", sin(M_PI / 2.0));

    return 0;
}

sin(0)      = 0.0  (0 degrees)
sin(M_PI/2) = 1.0  (90 degrees)

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

static double deg_to_rad(double degrees) {
    return degrees * M_PI / 180.0;
}

int main(void) {
    double angles[] = { 0.0, 30.0, 45.0, 60.0, 90.0 };
    size_t i;

    printf(" deg    sin()\n");
    for (i = 0; i < 5; i++) {
        double rad = deg_to_rad(angles[i]);
        printf("%4.0f  %6.3f\n", angles[i], sin(rad));
    }

    return 0;
}

 deg    sin()
   0   0.000
  30   0.500
  45   0.707
  60   0.866
  90   1.000

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

int main(void) {
    int deg;

    printf("deg   sin()\n");
    for (deg = 0; deg <= 90; deg += 15) {
        double rad = deg * M_PI / 180.0;
        printf("%3d  %6.3f\n", deg, sin(rad));
    }

    return 0;
}

deg   sin()
  0   0.000
 15   0.259
 30   0.500
 45   0.707
 60   0.866
 75   0.966
 90   1.000

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

int main(void) {
    double angles[] = { 0.0, M_PI / 2, M_PI };
    const char *labels[] = { "0", "pi/2", "pi" };
    size_t i;

    printf(" angle   sin()   cos()\n");
    for (i = 0; i < 3; i++) {
        printf(" %5s  %5.1f  %5.1f\n",
               labels[i], sin(angles[i]), cos(angles[i]));
    }

    return 0;
}

 angle   sin()   cos()
     0    0.0    1.0
  pi/2    1.0    0.0
    pi    0.0   -1.0

🚀 Common Use Cases

• Graphics and games — bobbing motion, pendulums, circular paths (y = r * sin(θ)).
• Audio synthesis — pure tones are sine waves at a given frequency.
• Physics — simple harmonic motion, springs, and pendulums.
• Signal processing — model periodic AC voltage and vibrations.
• Pair with cos() — full 2D position from angle and radius.

📝 Notes

• Input is radians, not degrees—convert with degrees * M_PI / 180.0.
• Output is always in [−1, 1].
• sin() is an odd function: sin(-x) == -sin(x).
• Link with -lm when using GCC/Clang on Unix-like systems.
• Do not confuse sin() with sinh() (hyperbolic sine).
• For very large angles, floating-point precision can affect results—consider reducing the angle modulo 2π if needed.

⚡ Optimization

sin() is implemented in the platform math library and is typically fast enough for most applications. If you call it thousands of times per frame in a game loop, profile first—often the bottleneck is elsewhere. For fixed small angle sets, a lookup table can help, but prefer the library function until profiling proves otherwise.

💡 Best Practices