# Arctan: Definition, Function & Formula

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• 0:00 Arctan as Inverse
• 0:45 When to Use Arctan
• 2:11 Example One
• 2:41 Example Two
• 2:55 Example Three
• 3:18 Lesson Summary

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Lesson Transcript
Instructor: Jennifer Beddoe
The arctan, or arctangent, is the inverse function of the tangent function. This lesson will define the arctan, describe its function, and take you through some examples.

## Arctan as Inverse

Every mathematical function has an inverse. Even simple operations such as addition and multiplication have inverses - subtraction and division. The arctan is the inverse of the tangent function and is used to compute the angle measure from the tangent ratio of a right triangle, designated by the formula:

The term 'arc' is used because when measuring an angle in radians, the arc length of a portion of a circle bisected by an angle (with the vertex at the center of the circle) equals the angle measure. The radian is the standard unit of measurement for an angle and is equal to approximately 57 degrees. It is based on the radius of a circle.

## When to Use Arctan

Trigonometric functions can be used to define values related to a right triangle. Practically, these functions can be used to determine heights of objects or distances that are difficult to measure. These measurements are determined using the measure of one angle (not the right angle) and a ratio of two sides of the triangle. Trigonometric functions are determined by the sides of the triangle that are used in the ratio of these formulas:

• sine = opposite / hypotenuse
• cosine = adjacent / hypotenuse
• tangent = opposite / adjacent

The inverse of these functions can be used to determine the angle measures when the sides of the triangle are known. You can use the arctan to determine an angle measure when the side opposite and the side adjacent to the angle are known. The arctan has practical applications in architecture, building, landscaping, physics, and engineering, among other scientific and mathematical areas.

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