YouTipRef Math Atan2
## Python math.atan2() Method
The `math.atan2()` method is a built-in function in Python's standard `math` module. It returns the arc tangent (inverse tangent) of the quotient $y / x$ in radians.
Unlike the standard `math.atan(y / x)` function, `math.atan2(y, x)` accepts both the $y$ and $x$ coordinates as separate arguments. This allows it to correctly determine the signs of both inputs and place the resulting angle in the correct quadrant of the Cartesian plane.
---
### Introduction to Quadrant Awareness
The returned value is a float representing the angle $\theta$ in radians between the positive x-axis and the point $(x, y)$.
* **Range:** The resulting angle is always between $-\pi$ and $\pi$ (inclusive of $-\pi$ and $\pi$, i.e., $[-\pi, \pi]$ radians, which corresponds to $-180^\circ$ to $180^\circ$).
* **Sign Handling:** It automatically handles the signs of $x$ and $y$ to resolve the correct quadrant, which a simple $y/x$ division cannot do (for example, distinguishing between $(-y)/(-x)$ in Quadrant III and $y/x$ in Quadrant I).
---
### Syntax
```python
import math
math.atan2(y, x)
```
#### Parameters
| Parameter | Type | Description |
| :--- | :--- | :--- |
| **`y`** | `float` or `int` | **Required.** The y-coordinate (vertical axis). Can be positive or negative. |
| **`x`** | `float` or `int` | **Required.** The x-coordinate (horizontal axis). Can be positive or negative. |
#### Return Value
* **Type:** `float`
* **Description:** Returns the arc tangent of $y/x$ in radians, ranging from $-\pi$ to $\pi$.
---
### Code Examples
#### Basic Usage
The following example demonstrates how to calculate the arc tangent for different coordinate pairs:
```python
import math
# Calculate the arc tangent of y/x
print(math.atan2(8, 5)) # Quadrant I (both positive)
print(math.atan2(20, 10)) # Quadrant I (both positive)
print(math.atan2(34, -7)) # Quadrant II (positive y, negative x)
```
**Output:**
```text
1.0121970114513341
1.1071487177940904
1.7738415440483617
```
---
### Advanced Examples & Considerations
#### 1. Converting Radians to Degrees
Because `math.atan2()` returns values in radians, you can use `math.degrees()` to convert the result into degrees ($0^\circ$ to $\pm180^\circ$):
```python
import math
radians = math.atan2(1, -1) # Quadrant II
degrees = math.degrees(radians)
print(f"Radians: {radians}")
print(f"Degrees: {degrees}°")
```
**Output:**
```text
Radians: 2.356194490192345
Degrees: 135.0°
```
#### 2. Handling Zero Values
Unlike standard division (`y / x`), which raises a `ZeroDivisionError` if $x = 0$, `math.atan2(y, x)` safely handles zero values:
```python
import math
# Point lies on the positive y-axis (90 degrees)
print(math.atan2(1, 0)) # Output: 1.5707963267948966 (pi / 2)
# Point lies on the negative y-axis (-90 degrees)
print(math.atan2(-1, 0)) # Output: -1.5707963267948966 (-pi / 2)
# Origin point (0, 0)
print(math.atan2(0, 0)) # Output: 0.0
```