Inverse Tangent Calculator

How to Calculate Inverse Tangent (arctan)

The inverse tangent function, also known as arctan or tan⁻¹, is used to find the angle whose tangent is a given value. It's the inverse operation of the tangent function.

Formula

The inverse tangent function is denoted as:

\[ \theta = \arctan(x) \]

Where:

• θ is the angle in radians
• x is the tangent value (any real number)

Calculation Steps

1. Input the tangent value x.
2. Use the arctan function to calculate the angle in radians.
3. If needed, convert the result to degrees using the formula: degrees = radians × (180/π).

Example

Let's calculate arctan(1):

1. Input: x = 1
2. Calculate arctan(1): \[ \theta = \arctan(1) = \frac{\pi}{4} \text{ radians} \]
3. Convert to degrees: \[ \frac{\pi}{4} \text{ radians} \times \frac{180°}{\pi} = 45° \]

Therefore, arctan(1) = π/4 radians or 45°.

Visual Representation

This diagram illustrates arctan(1). The blue arc represents the angle of 45°, and the red line shows the tangent value of 1 on the unit circle.