Mastering Math Class in Java: A Comprehensive Guide for ICSE Computer Application Students

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The `Math` class in Java is part of the `java.lang` package and provides a set of static methods for performing mathematical operations. Here's a list of some common functions available in the `Math` class:

1. **Basic Arithmetic Functions:**
- `addExact(int x, int y)` and `addExact(long x, long y)`: Adds two numbers, throwing an exception if the result overflows.
- `subtractExact(int x, int y)` and `subtractExact(long x, long y)`: Subtracts one number from another, throwing an exception if the result overflows.
- `multiplyExact(int x, int y)` and `multiplyExact(long x, long y)`: Multiplies two numbers, throwing an exception if the result overflows.
- `incrementExact(int a)` and `incrementExact(long a)`: Increments a number, throwing an exception if the result overflows.
- `decrementExact(int a)` and `decrementExact(long a)`: Decrements a number, throwing an exception if the result overflows.

2. **Rounding Functions:**
- `ceil(double a)`: Returns the smallest (closest to negative infinity) double value that is greater than or equal to the argument and is equal to a mathematical integer.
- `floor(double a)`: Returns the largest (closest to positive infinity) double value that is less than or equal to the argument and is equal to a mathematical integer.
- `round(float a)` and `round(double a)`: Returns the closest long or int to the argument, with ties rounding to positive infinity.

3. **Exponential and Logarithmic Functions:**
- `exp(double a)`: Returns Euler's number raised to the power of a double value.
- `log(double a)`: Returns the natural logarithm (base e) of a double value.
- `pow(double a, double b)`: Returns the value of the first argument raised to the power of the second argument.

4. **Trigonometric Functions:**
- `sin(double a)`, `cos(double a)`, and `tan(double a)`: Returns the sine, cosine, and tangent of an angle (in radians), respectively.
- `asin(double a)`, `acos(double a)`, and `atan(double a)`: Returns the arc sine, arc cosine, and arc tangent of a value, respectively.

5. **Other Utility Functions:**
- `sqrt(double a)`: Returns the correctly rounded positive square root of a double value.
- `abs(int a)`, `abs(long a)`, `abs(float a)`, and `abs(double a)`: Returns the absolute value of a number.