Arctan Calculator Negative

The arctangent function (also called inverse tangent) calculates the angle whose tangent is a given number. When dealing with negative values, the result depends on the quadrant in which the angle lies. This calculator helps you compute the arctan of negative numbers and understand the results.

What is Arctan?

The arctangent function, written as arctan(x) or tan⁻¹(x), is the inverse of the tangent function. It takes a ratio of the opposite side to the adjacent side of a right triangle and returns the angle in radians or degrees.

The range of the arctangent function is -π/2 to π/2 radians (-90° to 90°). This means that for any real number x, arctan(x) will always return an angle between these limits.

Formula: arctan(x) = θ where tan(θ) = x

Arctan of Negative Values

When you calculate the arctan of a negative number, the result is negative because the angle lies in the fourth quadrant of the unit circle. The tangent function is negative in the fourth quadrant because the sine is negative and the cosine is positive.

For example, arctan(-1) equals -π/4 radians (-45°). This means the angle is measured clockwise from the positive x-axis.

Key Point: The arctan of a negative number is always negative, reflecting the angle's position in the fourth quadrant.

How to Use This Calculator

Enter a negative number in the input field.
Select whether you want the result in radians or degrees.
Click "Calculate" to see the arctan of your number.
Review the result and interpretation.

The calculator will display the result in the selected unit and provide a brief explanation of what the value means.

Examples

Example 1: Basic Negative Arctan

Calculate arctan(-0.5) in radians.

Result: -0.4636 radians (approximately -26.565°)

Interpretation: The angle whose tangent is -0.5 is -0.4636 radians, which is in the fourth quadrant.

Example 2: Larger Negative Value

Calculate arctan(-2) in degrees.

Result: -63.4349°

Interpretation: The angle whose tangent is -2 is -63.4349°, also in the fourth quadrant.

FAQ

What is the range of the arctan function?: The range of the arctan function is -π/2 to π/2 radians (-90° to 90°).
Why is the arctan of a negative number negative?: The arctan of a negative number is negative because the angle lies in the fourth quadrant of the unit circle, where tangent is negative.
Can I use this calculator for complex numbers?: No, this calculator is designed for real numbers only. Complex numbers require a different approach.
How accurate are the results?: The calculator uses JavaScript's built-in Math.atan() function, which provides accurate results for real numbers.
Is there a difference between arctan and tan⁻¹?: Yes, arctan and tan⁻¹ represent the same function. The notation depends on the context and the field of study.