Inverse Tangent Calculator Degrees

The inverse tangent calculator (also called arctangent calculator) computes the angle whose tangent is the given number. This calculator works in degrees and provides both the angle and a visual representation of the tangent function.

What is Inverse Tangent?

The inverse tangent function, written as arctan(x) or tan⁻¹(x), is the inverse 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.

The range of the inverse tangent function is -90° to 90° because the tangent function is periodic with a period of 180° and symmetric about the origin. This means that for any real number x, there is exactly one angle θ between -90° and 90° whose tangent is x.

Note: The inverse tangent function is not defined for complex numbers. For complex numbers, the complex arctangent function is used.

How to Use the Calculator

Enter the value for which you want to find the inverse tangent in the input field.
Click the "Calculate" button to compute the result.
The calculator will display the angle in degrees and a visual representation of the tangent function.
Use the "Reset" button to clear the input and result.

Formula

The inverse tangent function is defined as:

arctan(x) = θ where tan(θ) = x and -90° ≤ θ ≤ 90°

The calculator uses the JavaScript Math.atan() function, which returns the arctangent in radians. The result is then converted to degrees by multiplying by 180/π.

Example Calculation

Let's calculate the inverse tangent of 1:

arctan(1) = θ where tan(θ) = 1 θ = 45°

This means that the angle whose tangent is 1 is 45 degrees. You can verify this by plugging 45 degrees into a tangent calculator.

Applications

The inverse tangent function has several practical applications:

Navigation: Used in GPS systems to calculate bearings and headings.
Engineering: Used in circuit analysis and signal processing.
Physics: Used in wave mechanics and optics.
Computer Graphics: Used in 3D rendering and perspective calculations.

FAQ

What is the range of the inverse tangent function?

The range of the inverse tangent function is -90° to 90° because the tangent function is periodic with a period of 180° and symmetric about the origin.

Can the inverse tangent function be used for complex numbers?

No, the inverse tangent function is not defined for complex numbers. For complex numbers, the complex arctangent function is used.

What is the difference between arctan and tan⁻¹?

There is no difference between arctan and tan⁻¹. Both notations represent the inverse tangent function.