# ATAN2

The ATAN2 function returns the arctangent of the specified x- and y-coordinates, representing the angle in radians between the positive x-axis and the point (x, y) in the Cartesian plane.

## Syntax

=ATAN2(`x_num`

, `y_num`

)

`x_num` | The x-coordinate of the point in the Cartesian plane. |

`y_num` | The y-coordinate of the point in the Cartesian plane. |

## About ATAN2

When dealing with the intricacies of trigonometry and angular calculations in Excel, the ATAN2 function comes to your aid. It serves the purpose of determining the arctangent of the ratio of two specified numbers, primarily utilized for finding the angle theta in the polar coordinate system. This function proves invaluable in various engineering, physics, and mathematical applications requiring precise angle calculations and vector analysis. Moreover, ATAN2 provides a reliable mechanism for handling points with negative or zero coordinates, ensuring accurate angle determination across all quadrants of the Cartesian plane. Embracing the flexibility of radians as its output unit, ATAN2 seamlessly adapts to a wide array of mathematical scenarios, empowering users to perform advanced geometric computations with ease and confidence.

## Examples

Suppose you have a point with the coordinates (4, 3) in the Cartesian plane. To calculate the angle theta in radians, you would use the ATAN2 formula as follows: =ATAN2(4, 3) This will return the value of approximately 0.93 radians, representing the angle between the positive x-axis and the point (4, 3).

Consider a point with the coordinates (-2, -5) in the Cartesian plane. To find the angle theta in radians, the ATAN2 formula would be: =ATAN2(-2, -5) This will yield a value of approximately -2.60 radians, signifying the angle between the positive x-axis and the point (-2, -5).

## Notes

The ATAN2 function outputs the angle in radians, reflecting the standard unit for angular measurement in mathematical and scientific contexts. Ensure that the coordinates provided as arguments align with the conventions of the Cartesian plane, with positive x-coordinates extending towards the right and positive y-coordinates stretching upwards. ATAN2 seamlessly handles inputs with negative or zero values, delivering accurate angle results across the entire range of possible coordinate combinations.

## Questions

**What is the output unit of the angle returned by the ATAN2 function?**

The ATAN2 function returns the angle in radians, adhering to the standard unit for angular measurement across mathematical and scientific domains.

**In what scenarios is the ATAN2 function particularly beneficial?**

The ATAN2 function proves immensely valuable in applications requiring precise angle calculations and vector analysis. It is extensively used in engineering, physics, and mathematical contexts for advanced geometric computations and angular determinations.

**How does the ATAN2 function handle points with negative or zero coordinates?**

ATAN2 seamlessly handles points with negative or zero coordinates, ensuring accurate angle determination across all quadrants of the Cartesian plane. It possesses the capability to handle a diverse range of coordinate combinations, delivering reliable results in various mathematical scenarios.