- 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.
- Write the corresponding set of inverse trigonometric methods that return their values in degrees instead of radians.
- The math library is missing secant, cosecant and cotangent methods. Write them.
- The math library lacks a log10 method for taking the common logarithm. Write one.
- Computer scientists often use a log2 (log base 2). java.lang.Math doesn't have one of those either. Write it.
- Put all the methods in the previous five exercises into a package and class of your own creation. Be sure to choose sensible, easy-to-understand, hard-to-confuse, names for all packages, classes, and methods. Declare methods and fields static, final, and/or abstract when appropriate.
- 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 p0 * e to the 1.4t. 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.
- Modify the bacteria growth program so that the time can be input in minutes. Note that the formula still requires a time in hours.
- Complete the
`ComplexNumber`

class discussed in last week's class. - Define a reasonably named package for financial classes. Place
last week's
`Money`

class in this package. - Add an overloaded constructor to the
`Money`

class that only takes the number of dollars. - Add an overloaded constructor to the
`Money`

class that takes no arguments and initializes the object to $0.00. - Add an
`equals()`

method to the`Money`

class. - Define an exception class called
`MoneyOverflowException`

which can be thrown when an operation with`Money`

results in an over flow. Place this class in the same finance package. - Rewrite the methods in the
`Money`

class so that they recognize overflow and throw a`MoneyOverFlowException`

if it occurs. - Use the classes in the
`java.math`

package to eliminate the possibility of overflow in the`Money`

class. - Rewrite the two logistic equation problems from Week 2 using
the
`java.math.BigDecimal`

class to provide 20 decimal digits of precision. Some hints:- Invocation of the
`setScale()`

method with every iteration is necessary to keep the value of population from overflawing the memory of the computer. - You may need to use
`compareTo()`

and the`Comparable`

interface instead of either`==`

or`equals()`

.

- Invocation of the