Chapter 8: Packages

Quiz

1. What happens if you try to take the square root of a negative number?

   Java returns NaN, an IEEE invention that means "Not a Number."

2. What happens if you use java.lang.Math.pow() to raise zero to the zeroth power?

   Java returns 1. Mathematically, this is incorrect. It should return NaN.

3. What, if anything, can come before a package statement in a Java source code file?

   Only comments.

4. What, if anything, can come before an import statement in a Java source code file?

   Comments and package statements.

5. Can one source code file import from more than one package?

   Absolutely.

Exercises

1. Although mathematicians prefer to work in radians, most scientists and engineers find it easier to think in degrees. Write sine, cosine and tangent methods that accept their arguments in degrees.

   public double sine(double degrees) {
   
     double radians = degrees * Math.PI / 180.0;
     return Math.sin(radians);
     
   }
   
   public double cosine(double degrees) {
   
     double radians = degrees * Math.PI / 180.0;
     return Math.cos(radians);
     
   }
   
   public double tangent(double degrees) {
   
     double radians = degrees * Math.PI / 180.0;
     return Math.tan(radians);
     
   }
   

2. Write the corresponding set of inverse trigonometric methods that return their values in degrees instead of radians.

   public double arcsine(double sine) {
   
     return Math.asin(sine) * 180.0 / Math.PI;
     
   }
   
   public double arccosine(double cosine) {
   
     return Math.acos(cosine) * 180.0 / Math.PI;
     
   }
   
   public double arctangent(double tangent) {
   
     return Math.atan(tangent) * 180.0 / Math.PI;
     
   }
   

3. The math library is missing secant, cosecant and cotangent methods. Write them.

   public double sec(double radians) {
   
     return 1.0/Math.cos(radians);
     
   }
   
   public double csc(double radians) {
   
     return 1.0/Math.sin(radians);
     
   }
   
   public double ctn(double radians) {
   
     return 1.0/Math.tan(radians);
     
   }
   

4. The math library lacks a log10 method for taking the common logarithm. Write one.

   public double log10(double x) {
   
     return Math.log(x)/Math.log(10.0);
     
   }
   

5. Computer scientists often use a log2 (log base 2). java.lang.Math doesn't have one of those either. Write it.

   public double log2(double x) {
   
     return Math.log(x)/Math.log(2.0);
     
   }
   

6. A simple model for the growth of bacteria with an unlimited supply of nutrients says that after t hours an initial population of p0 will have grown to p0e1.4t. Write a Java application that calculates the growth of a colony of bacteria. As usual get the value of p0 and t from the command line.

   public class bacteria {
   
     public static void main(String args[])  {
     
       try {
         double p0 = Double.valueOf(args[0]).doubleValue();
         double t = Double.valueOf(args[1]).doubleValue();
         System.out.println(p0 * Math.exp(1.4 * t)); 
       }
       catch (Exception e) {
         System.out.println("Usage: java bacteria initial_population num_hours");
       
       }
       
     }
   
   }

7. Modify the bacteria growth program so that the time can be input in minutes. Note that the formula still requires a time in hours.

   public class bacteria {
   
     public static void main(String args[])  {
     
       try {
         double p0 = Double.valueOf(args[0]).doubleValue();
         double t = Double.valueOf(args[1]).doubleValue()/60.0;
         System.out.println(p0 * Math.exp(1.4 * t));
       }
       catch (Exception e) {
         System.out.println("Usage: java bacteria initial_population num_hours");
       
       }
       
     }
   
   }

8. Carbon dating is used to estimate the age of once living objects according to the following formula:

   Write a Java application that calculates the age of an object given the percentage of carbon 14 remaining.

   public class agefromC14 {
   
     public static void main(String args[])  {
     
       try {
         double p0 = Double.valueOf(args[0]).doubleValue();
         double age = -Math.log(p0/1.22E-4);
         System.out.println(age);
     
       }
       catch (Exception e) {
         System.out.println("Usage: java agefromC14 %_C14");
       
       }
       
     }
   
   }

9. Put the VeryLong and Rational classes of the Exercises in Chapter 7 into your own package.