Arctan Degrees Calculator
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Reviewed by Calculator Editorial Team
The arctan degrees calculator computes the inverse tangent of a number in degrees. This is useful for finding angles in right triangles, solving trigonometric equations, and various scientific and engineering applications.
What is Arctan?
The arctangent function, also known as the inverse tangent function, is the inverse of the tangent function. While the tangent function takes an angle and returns a ratio of sides of a right triangle, the arctangent function takes a ratio and returns the angle.
In mathematical terms, if tan(θ) = y/x, then θ = arctan(y/x). The result is typically given in radians, but our calculator provides the angle in degrees for easier interpretation.
Note: The arctan function has a range of -90° to 90°, meaning it cannot distinguish between angles in different quadrants that have the same tangent value.
How to Use the Calculator
- Enter the value for which you want to calculate the arctangent.
- Click the "Calculate" button to compute the result.
- Review the result in degrees and the visual representation on the chart.
- Use the "Reset" button to clear the calculator for new calculations.
The calculator handles both positive and negative values, providing results in the appropriate degree range.
Formula
The arctangent of a number x in degrees is calculated using the following formula:
arctan(x) = atan(x) × (180/π)
Where:
- atan(x) is the arctangent function in radians
- 180/π is the conversion factor from radians to degrees
Examples
| Input Value | Arctan (Degrees) | Interpretation |
|---|---|---|
| 1 | 45° | For a right triangle with opposite side 1 and adjacent side 1, the angle is 45°. |
| 0 | 0° | When the ratio is zero, the angle is zero degrees. |
| -1 | -45° | Negative values result in negative angles. |
Interpreting Results
The result from the arctan degrees calculator represents the angle whose tangent is equal to the input value. This angle is measured in degrees and lies between -90° and 90°.
For practical applications:
- Positive results indicate angles in the first quadrant (0° to 90°).
- Negative results indicate angles in the fourth quadrant (-90° to 0°).
- For angles outside this range, additional information about the quadrant is needed.
FAQ
- What is the difference between arctan and tan?
- The tangent function (tan) takes an angle and returns a ratio, while the arctangent function (arctan) takes a ratio and returns an angle. They are inverse operations.
- Why does the calculator only show angles between -90° and 90°?
- The arctangent function has a range of -90° to 90° because the tangent function is periodic with a period of 180°. For angles outside this range, you would need additional information about the quadrant.
- Can I use this calculator for complex numbers?
- No, this calculator is designed for real numbers only. Complex numbers require a different approach using logarithms.
- How accurate are the results?
- The calculator uses JavaScript's built-in Math.atan() function, which provides results accurate to approximately 15 decimal places.
- Is there a mobile app version of this calculator?
- Currently, this calculator is available as a web application. We may develop a mobile app in the future based on user demand.