Tan Inverse Calculator
Use this calculator to find the angle (in both radians and degrees) when you know the tangent of that angle. This is also known as the arctangent function (atan).
Understanding the Tan Inverse Function (Arctangent)
The tan inverse function, often written as arctan(x) or tan-1(x), is the inverse operation of the tangent function. While the tangent function takes an angle and returns the ratio of the opposite side to the adjacent side in a right-angled triangle, the tan inverse function does the opposite: it takes that ratio (the tangent value) and returns the corresponding angle.
What is Arctan Used For?
- Finding Angles in Right Triangles: If you know the lengths of the opposite and adjacent sides relative to an angle in a right triangle, you can find the angle using arctan(opposite/adjacent).
- Trigonometry and Geometry: It's fundamental in solving various geometric and trigonometric problems where angles need to be determined from side ratios.
- Calculus: The arctangent function appears in integral calculus, particularly when integrating rational functions.
- Physics and Engineering: Used in vector analysis, determining angles of forces, trajectories, and electrical phase angles.
Radians vs. Degrees
Angles can be measured in two primary units: degrees and radians.
- Degrees: A full circle is 360 degrees. It's commonly used in everyday geometry and many practical applications.
- Radians: A full circle is 2π radians. Radians are the standard unit for angles in advanced mathematics, physics, and engineering because they simplify many formulas, especially in calculus. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius.
This calculator provides the result in both units for your convenience.
Example Calculation:
Let's say you have a right-angled triangle where the side opposite an angle is 5 units long, and the adjacent side is also 5 units long. The tangent of this angle would be 5/5 = 1.
Using the tan inverse calculator with an input of 1:
- The angle in radians would be approximately 0.7854 radians.
- The angle in degrees would be exactly 45 degrees.
This makes sense, as an angle where the opposite and adjacent sides are equal is a 45-degree angle.