1. How do you import the math module and call functions in that library?
2. To the best of your mathematical ability, describe what each of the listed functions in the math module will do. Give some sample input and output (if known).
3. What two common math constants are part of the math module? How do you use them in your code?
4. Which useful math-related functions can be found in the core Python library? How do you call those functions?
What does each core function do? What are some sample inputs and outputs?
1. To import the math module in Python, you can use the following statement:
```python
import math
```
Once you have imported the math module, you can call functions from that library using the syntax `math.function_name()`.
2. Some of the functions in the math module and their descriptions are:
- `math.sqrt(x)`: Returns the square root of x.
Sample input: `math.sqrt(16)`
Output: `4.0`
- `math.sin(x)`: Returns the sine of x (in radians).
Sample input: `math.sin(math.pi/2)`
Output: `1.0`
- `math.cos(x)`: Returns the cosine of x (in radians).
Sample input: `math.cos(0)`
Output: `1.0`
3. Two common math constants in the math module are `math.pi` and `math.e`. You can use them in your code directly by referencing `math.pi` and `math.e`, for example:
```python
radius = 5
circumference = 2 * math.pi * radius
```
4. Some useful math-related functions in the core Python library (built-in functions) include `abs()`, `round()`, and `min()/max()`. These functions can be called directly without importing any modules.
- `abs(x)`: Returns the absolute value of x.
Sample input: `abs(-5)`
Output: `5`
- `round(x)`: Returns x rounded to the nearest integer.
Sample input: `round(3.14159, 2)`
Output: `3.14`
- `min(iterable)`: Returns the smallest element in an iterable.
Sample input: `min([3, 1, 5, 2])`
Output: `1`
- `max(iterable)`: Returns the largest element in an iterable.
Sample input: `max([3, 1, 5, 2])`
Output: `5`