C Math tan() Function

What You’ll Learn

The tan() function computes the tangent of an angle in radians—the ratio of opposite to adjacent on a right triangle, or sin/cos on the unit circle. Essential for slopes, rotations, and graphics.

Definition and Usage

Tangent is opposite ÷ adjacent on a right triangle. Equivalently, tan(θ) = sin(θ) / cos(θ) when cos(θ) ≠ 0.

In C, tan(x) expects x in radians. At 45° (π/4 radians), opposite equals adjacent, so tan(M_PI / 4) is 1.0.

📝 Syntax

Standard C declaration:

double tan(double x);

Related variants

float tanf(float x);             /* <math.h> */
long double tanl(long double x); /* <math.h> */

Parameters

• x — angle in radians.

Return Value

• Tangent of x as double (unbounded).
• tan(0) returns 0.0; tan(M_PI / 4) returns 1.0.
• Near cos(x) = 0, result may be huge or INFINITY.

Headers and linking

• #include <math.h>
• Compile: gcc tan.c -std=c11 -o tan -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 are in radians unless converted from degrees explicitly.

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

int main(void) {
    double angle_rad = M_PI / 4.0;
    double result = tan(angle_rad);

    printf("Tangent of 45 degrees: %.6f\n", result);

    return 0;
}

Tangent of 45 degrees: 1.000000

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

int main(void) {
    double rad = M_PI / 3.0;

    printf("angle = pi/3 (60 degrees)\n");
    printf("tan(x)     = %.6f\n", tan(rad));
    printf("sin/cos    = %.6f\n", sin(rad) / cos(rad));

    return 0;
}

angle = pi/3 (60 degrees)
tan(x)     = 1.732051
sin/cos    = 1.732051

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

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

    printf(" deg    tan()\n");
    for (i = 0; i < 4; i++) {
        double rad = degs[i] * M_PI / 180.0;
        printf("%4.0f  %6.3f\n", degs[i], tan(rad));
    }

    return 0;
}

 deg    tan()
   0   0.000
  30   0.577
  45   1.000
  60   1.732

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

int main(void) {
    double rise = 3.0;
    double run = 4.0;
    double angle_rad = atan2(rise, run);
    double angle_deg = angle_rad * 180.0 / M_PI;

    printf("Rise: %.0f, Run: %.0f\n", rise, run);
    printf("Slope tan = %.3f\n", tan(angle_rad));
    printf("Angle: %.1f degrees\n", angle_deg);

    return 0;
}

Rise: 3, Run: 4
Slope tan = 0.750
Angle: 36.9 degrees

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

int main(void) {
    double vals[] = { 0.0, 0.5, 1.0, 1.5 };
    size_t i;

    printf("   x     tan(x)   tanh(x)\n");
    for (i = 0; i < 4; i++) {
        double x = vals[i];
        printf("%4.1f  %8.4f  %8.4f\n", x, tan(x), tanh(x));
    }

    return 0;
}

   x     tan(x)   tanh(x)
 0.0    0.0000    0.0000
 0.5    0.5463    0.4621
 1.0    1.5574    0.7616
 1.5    14.1014    0.9051

🚀 Common Use Cases

• Graphics and games — rotation angles, slope of lines, camera tilt.
• Physics — incline problems, force components on ramps.
• Engineering — roof pitch, grade percent, structural angles.
• Navigation — bearing calculations with atan2.
• Pair with atan2() — recover angle from rise and run.

📝 Notes

• Input is radians, not degrees—convert with degrees * M_PI / 180.0.
• tan(x) = sin(x) / cos(x) when cos(x) ≠ 0.
• Undefined at π/2, 3π/2, … (90°, 270°, …).
• Output is unbounded—not limited to [−1, 1] like sin/cos.
• Do not confuse tan() with tanh() (hyperbolic).
• Link with -lm on GCC/Clang Unix-like builds.

⚡ Optimization

tan() is implemented in the platform math library. If you already have sin and cos for the same angle, some libraries compute both together—but calling tan directly is fine unless profiling says otherwise. For angle-from-vector work, atan2 is the right inverse tool.

💡 Best Practices