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Java - Math.acos() method example

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Created by:

Warren-X

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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.

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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:

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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

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Syntax	xxxxxxxxxx 1 package java.lang; 2 3 public final class Math { 4 5 public static double acos(double number) { ... } 6 7 } 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

Edit

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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
    }
}
​