C acos() Function
Definition
In C, acos() returns the angle whose cosine is x. The angle is in radians, from 0 to π. acos(1) is 0, and acos(0) is π/2.
You pass one double. It must be from -1 to 1. The result is a double in radians, not degrees. Include <math.h>.
Syntax
Pass a cosine from -1 to 1. Start with this call.
| Call | What it does |
|---|
acos(0.0) | Returns π/2, the angle whose cosine is 0. |
Include <math.h>. On GCC, link with -lm. The result is radians.
Library declarations
double acos(double x);
float acosf(float x);
long double acosl(long double x);
Parameters
| Parameter | Description |
|---|
| x | Required. A cosine from -1 to 1. |
Return Value
| Return Value | Description |
|---|
| Radians | The angle from 0 to π whose cosine is x. |
| NaN | Returned when x is outside -1 to 1. |
C Examples
Example 1 — Common acos Values
Print radians for a few cosine inputs in the valid domain.
#include <math.h>
#include <stdio.h>
int main(void) {
printf("acos(1) = %.4f\n", acos(1.0));
printf("acos(0) = %.4f\n", acos(0.0));
printf("acos(0.5) = %.4f\n", acos(0.5));
printf("acos(-1) = %.4f\n", acos(-1.0));
return 0;
}
acos(1) = 0.0000
acos(0) = 1.5708
acos(0.5) = 1.0472
acos(-1) = 3.1416
How It Works
- Include math.h. Declares
acos; link with -lm on GCC. - Endpoints.
acos(1) is 0; acos(-1) is π. - Middle values.
acos(0) is π/2; acos(0.5) is π/3. - Units are radians. These numbers are not degrees until you convert.
Example 2 — Convert Radians to Degrees
Multiply by 180 / π when you want a degree reading.
#include <math.h>
#include <stdio.h>
int main(void) {
double x = 0.5;
double rad = acos(x);
double pi = acos(-1.0);
double deg = rad * 180.0 / pi;
printf("acos(%.1f) = %.4f rad\n", x, rad);
printf(" = %.2f deg\n", deg);
return 0;
}
acos(0.5) = 1.0472 rad
= 60.00 degHow It Works
- Get radians first.
acos(0.5) ≈ 1.0472. - Get π portably.
acos(-1.0) equals π without needing M_PI. - Scale to degrees. Multiply by
180.0 / pi → 60. - Keep rad for math. Pass radians into
cos/sin; use degrees only for display.
Example 3 — Portable π with acos(-1)
A common ISO-friendly way to define π when M_PI is missing.
#include <math.h>
#include <stdio.h>
int main(void) {
const double PI = acos(-1.0);
printf("PI ≈ %.10f\n", PI);
printf("cos(PI/3) ≈ %.4f\n", cos(PI / 3.0));
return 0;
}
PI ≈ 3.1415926536
cos(PI/3) ≈ 0.5000
How It Works
- Ask for acos(-1). That angle is exactly π radians.
- Store as a constant. Reuse
PI for conversions and trig. - Check with cos.
cos(π/3) should be about 0.5. - Inverse pair.
cos and acos undo each other on the valid domain.
Frequently Asked Questions
acos() returns the angle, in radians, whose cosine is x. acos(1) is 0 and acos(0) is π/2.
x is required. It is a double from -1 to 1.
A double in radians, from 0 to π. If x is outside -1 to 1, the result is NaN.
Include <math.h>. On GCC, link with -lm.
No. The result is radians. Multiply by 180/π when you want degrees.
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