Java - Math.acos() method example

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

package java.lang;

public final class Math {

    public static double acos(double number) { ... }

}

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