Inverse Tan Degrees Calculator
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Reviewed by Calculator Editorial Team
The inverse tangent function, also known as arctan, calculates the angle whose tangent is a given number. This calculator computes the inverse tangent in degrees, providing both the principal value and the result in degrees.
What is Inverse Tan?
The inverse tangent function (arctan) is the inverse operation of the tangent function. While the tangent function takes an angle and returns a ratio, the inverse tangent takes a ratio and returns an angle. This is particularly useful in trigonometry, physics, and engineering.
Inverse tangent is periodic with a period of 180 degrees, meaning it will return values between -90 and 90 degrees. The principal value is the angle between -90 and 90 degrees that satisfies the equation.
The inverse tangent function is often used to find angles in right triangles when only the ratio of the opposite side to the adjacent side is known.
How to Use the Calculator
Using the inverse tan degrees calculator is straightforward:
- Enter the value for which you want to calculate the inverse tangent.
- Click the "Calculate" button to compute the result.
- View the result in degrees, which represents the angle whose tangent is the entered value.
- Use the "Reset" button to clear the input and result.
The calculator will display the result in degrees and provide a visual representation of the angle on a unit circle.
Formula
The inverse tangent function in degrees is calculated using the following formula:
Where:
- x is the input value for which you want to find the inverse tangent.
- atan(x) is the inverse tangent function in radians.
- 180/π is the conversion factor from radians to degrees.
The result is the angle in degrees whose tangent is the input value.
Examples
Let's look at a few examples to understand how the inverse tangent function works:
| Input (x) | arctan(x) in Degrees | Interpretation |
|---|---|---|
| 1 | 45.00° | The angle whose tangent is 1 is 45 degrees. |
| 0.5 | 26.57° | The angle whose tangent is 0.5 is approximately 26.57 degrees. |
| -1 | -45.00° | The angle whose tangent is -1 is -45 degrees. |
These examples illustrate how the inverse tangent function converts a ratio into an angle in degrees.
FAQ
What is the range of the inverse tangent function in degrees?
The inverse tangent function in degrees returns values between -90 and 90 degrees. This is because the tangent function is periodic with a period of 180 degrees.
How do I calculate the inverse tangent of a negative number?
The inverse tangent of a negative number will return a negative angle between -90 and 0 degrees. For example, arctan(-1) = -45 degrees.
Can the inverse tangent function be used to find angles in non-right triangles?
Yes, the inverse tangent function can be used in any triangle to find angles when you know the ratio of the opposite side to the adjacent side. This is particularly useful in trigonometric calculations.