Inverse Tan Calculator in Degrees

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 angle and a visual representation of the relationship between the angle and its tangent value.

What is Inverse Tan?

The inverse tangent function, often written as arctan or tan⁻¹, is the inverse of the tangent function. While the tangent function takes an angle and returns a ratio, the inverse tangent function takes a ratio and returns an angle.

In trigonometry, the tangent of an angle θ in a right-angled triangle is the ratio of the opposite side to the adjacent side (tanθ = opposite/adjacent). The inverse tangent function reverses this relationship by finding the angle θ given the ratio of opposite to adjacent sides.

The inverse tangent function is periodic with a period of π radians (180 degrees), meaning it will return the same angle for any ratio that repeats every 180 degrees. The range of the inverse tangent function is typically restricted to -π/2 to π/2 radians (-90° to 90°).

How to Use the Calculator

Enter the ratio (opposite/adjacent) in the input field.
Click the "Calculate" button to compute the angle in degrees.
View the result, which includes the angle in degrees and a visual representation of the relationship.
Use the "Reset" button to clear the input and result.

Formula

The inverse tangent function in degrees is calculated using the following formula:

arctan(x) = atan(x) × (180/π)

Where:

x is the ratio of the opposite side to the adjacent side.
atan(x) is the inverse tangent function in radians.
180/π is the conversion factor from radians to degrees.

Examples

Example 1

If the ratio of the opposite side to the adjacent side is 1, the angle is:

arctan(1) = atan(1) × (180/π) = 45°

Example 2

If the ratio is 0.5, the angle is approximately:

arctan(0.5) ≈ atan(0.5) × (180/π) ≈ 26.565°

Applications

The inverse tangent function has numerous applications in various fields:

Engineering: Used in designing and analyzing structures, such as bridges and buildings.
Physics: Applied in calculating angles in projectile motion and wave analysis.
Computer Graphics: Used in 3D modeling and rendering to determine angles and orientations.
Navigation: Helps in calculating bearings and directions in GPS and map applications.
Statistics: Used in regression analysis to determine correlation coefficients.

FAQ

What is the range of the inverse tangent function?: The inverse tangent function typically returns values between -90° and 90°.
How do I convert radians to degrees?: Multiply the radian value by 180/π to convert it to degrees.
What is the difference between tan and arctan?: The tangent function (tan) takes an angle and returns a ratio, while the inverse tangent function (arctan) takes a ratio and returns an angle.
Can the inverse tangent function be used for negative ratios?: Yes, the inverse tangent function can handle negative ratios and returns angles in the appropriate quadrant.