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# Java - Math.acos() method example

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The `Math.acos` function returns number in radians in the range 0 to Math.PI. Based on this function we are able to calculate the inverted cosine function value.

``````public class CustomMath {

public static void main(String[] args) {
System.out.println( Math.acos( -2   ) ); // NaN
System.out.println( Math.acos( -1   ) ); // 3.1415926535897930 ->  180
System.out.println( Math.acos( -0.5 ) ); // 2.0943951023931957 -> ~120
System.out.println( Math.acos(  0   ) ); // 1.5707963267948966 ->   90
System.out.println( Math.acos(  0.5 ) ); // 1.0471975511965979 ->  ~60
System.out.println( Math.acos(  1   ) ); // 0                  ->    0
System.out.println( Math.acos(  2   ) ); // NaN

System.out.println( Math.acos(  0.7071067811865476   ) ); // 0.7853981633974483 -> 45 deg
System.out.println( Math.acos(  0.8660254037844387   ) ); // 0.5235987755982987 -> 30 deg

System.out.println(Math.acos(  Math.cos(  Math.PI / 4))); // 0.7853981633974483 -> pi/4 (45deg)
System.out.println(Math.cos(   Math.acos( Math.PI / 4))); // 0.7853981633974483 -> pi/4 (45deg)
}
}``````

Another way to look at `acos` function:

``````public class CustomMath {

static double calculateAngle(double b, double h) {
return Math.acos(b / h);
}

public static void main(String[] args) {
/*

|\
| \ h
a |  \
|__*\ <- angle
b

*/

double a, b, h;

// a, b and h build isosceles right triangle
a = 3;
b = a;
h = Math.sqrt(a * a + b * b);
System.out.println( CustomMath.calculateAngle(b, h) ); // 0.7853981633974483 <-  45 degrees

// a, b and h build half of equilateral triangle
a = 3;
b = a * Math.sqrt(3);
h = Math.sqrt(a * a + b * b);
System.out.println( CustomMath.calculateAngle(b, h) ); // 0.5235987755982987 <- ~30 degrees

// a, b and h are not able to build triangle
a = 3;
b = a;
h = 1;
System.out.println( CustomMath.calculateAngle(b, h) ); // NaN
}
}``````

## 1. Documentation

 Syntax ``````package java.lang; public final class Math { public static double acos(double number) { ... } }`````` Note: Classes in the `java.lang` package are imported automatically, so it is not necessary to do it manually - we use just `Math.acos()` call. Parameters `number` - double value that represents the result of the operation `adjacent / hypotenuse` on the right triangle. `number` should be in the range `-1` to `+1`. Result `number` value in radians in the range `0` to `Math.PI` (primitive value). If the value can not be calculated `NaN` is returned. Description `acos` is a static method that takes only one parameter and returns an approximation of the result of the mathematical function arccosine(x).

## 2. Working with degrees

``````public class CustomMath {

static double calculateAngle(double b, double h) {
double angle = Math.acos(b / h);

return (180 / Math.PI) * angle; // rad to deg conversion
}

public static void main(String[] args) {
/*
|\
| \ h
a |  \
|__*\ <- angle
b
*/

double a, b, h;

// a, b and h build isosceles right triangle
a = 3;
b = a;
h = Math.sqrt(a * a + b * b);
System.out.println( calculateAngle(b, h) ); // 45 degrees

// a, b and h build half of equilateral triangle
a = 3;
b = a * Math.sqrt(3);
h = Math.sqrt(a * a + b * b);
System.out.println( calculateAngle(b, h) ); // ~30 degrees

// a, b and h are not able to build triangle
a = 3;
b = a;
h = 1;
System.out.println( calculateAngle(b, h) ); // NaN
}
}
``````

## References

1. Inverse trigonometric functions - Wikipedia

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