A Tan Inverse Calculator (also called an Arctan Calculator) helps you find the inverse tangent (arctan) of a given number. The inverse tangent function, written as tan⁻¹(x) or arctan(x), determines the angle whose tangent is x.
In simpler terms, if you know the ratio of the opposite side to the adjacent side of a right triangle, the arctangent will give you the angle.
Table of Contents
What is Tangent?
Before diving into the inverse, let’s quickly review tangent. In a right triangle, the tangent of an angle (θ) is defined as:
tan(θ) = opposite / adjacent
What is Arctangent?
Arctangent (arctan or tan⁻¹) is the inverse function of tangent. It answers the question: “What angle has this tangent value?”
θ = arctan(opposite / adjacent)How to Use the Tan Inverse Calculator
- Enter the value of x (the tangent value).
- Select the desired unit (degrees or radians).
- Click “Calculate” to get the inverse tangent (angle).
- View the result, displayed in both degrees and radians.
Common Arctangent Values
| Tangent Value | Angle (Degrees) | Angle (Radians) |
|---|---|---|
| 0 | 0° | 0 |
| 1 | 45° | π/4 |
| √3 | 60° | π/3 |
| 1/√3 | 30° | π/6 |
Example Calculations
| Tangent Value (x) | Arctan(x) in Degrees | Arctan(x) in Radians |
|---|---|---|
| 1.0 | 45° | 0.7854 rad |
| 0.5 | 26.57° | 0.4636 rad |
| -1.0 | -45° | -0.7854 rad |
| √3 | 60° | 1.0472 rad |
| -√3 | -60° | -1.0472 rad |
Key Considerations
- Domain and Range: The domain of arctangent is all real numbers, and the range is (-π/2, π/2) radians or (-90°, 90°) degrees.
- Quadrant: Arctangent provides angles in the first and fourth quadrants. To find angles in other quadrants, you might need to add or subtract multiples of π (or 180°).
- Units: Ensure your calculator is set to the correct units (degrees or radians).
FAQs
🔹 What is the range of the arctan function?
The range of tan⁻¹(x) is from -90° to 90° (or -π/2 to π/2 in radians).
🔹 What is tan⁻¹(1)?
Tan⁻¹(1) = 45° or π/4 radians.
🔹 Can arctan be negative?
Yes, when x is negative, arctan(x) returns a negative angle.
🔹 How do I calculate arctan on a calculator?
Use the tan⁻¹ or arctan button on a scientific calculator, or use an online Tan Inverse Calculator.
🔹 Is arctan the same as 1/tan?
No, arctan(x) ≠ 1/tan(x). Instead, arctan(x) finds the angle whose tangent is x.
References
- National Institute of Standards and Technology: NIST Digital Library – Gives detailed information about the mathematical definitions and properties of trigonometric functions, including Tan Inverse.