# Tangent Calculator

Calculate the tangent of any angle in degrees or radians. Find tan, arctan, and cotangent values instantly. Handles undefined cases.

## What this calculates

Calculate the tangent of any angle in degrees or radians. Get the tan value, its inverse (arctan), the cotangent, and related angle information. The calculator handles undefined values at 90° and 270°.

## Inputs

- **Angle** — The angle to evaluate.
- **Angle Unit** — options: Degrees, Radians — Select degrees or radians.

## Outputs

- **tan(θ)** — formatted as text — The tangent of the angle. Undefined at 90° and 270°.
- **arctan (degrees)** — The inverse tangent of the result, in degrees.
- **cot(θ)** — formatted as text — The cotangent (1/tan or cos/sin). Undefined when sin = 0.
- **Related Angle Info** — formatted as text — The angle in the other unit and its quadrant.

## Details

The tangent function is defined as the ratio of sine to cosine: tan(θ) = sin(θ)/cos(θ). For a right triangle, tan(θ) equals the ratio of the opposite side to the adjacent side. Unlike sine and cosine, tangent has no upper or lower bound; its range is all real numbers.

Tangent has a period of 180° (π radians) and is undefined at 90° and 270° (where cosine is zero). It has vertical asymptotes at these angles. Tangent is positive in Quadrants I and III (where sine and cosine have the same sign) and negative in Quadrants II and IV.

The inverse tangent function, arctan(x) or tan⁻¹(x), returns the angle whose tangent is x. Unlike arcsin and arccos, arctan is defined for all real numbers and returns values in (-90°, 90°). The cotangent, cot(θ) = 1/tan(θ) = cos(θ)/sin(θ), is the reciprocal of tangent and is undefined when sin(θ) = 0.

## Frequently Asked Questions

**Q: What is the tangent function?**

A: Tangent is sin(θ)/cos(θ), or equivalently the ratio of the opposite to adjacent side in a right triangle. Its range is all real numbers (unlike sin and cos which are bounded between -1 and 1). It has a period of 180°.

**Q: Why is tangent undefined at 90° and 270°?**

A: At 90° and 270°, cos(θ) = 0, and since tan = sin/cos, this involves division by zero. The tangent function approaches positive or negative infinity near these angles, creating vertical asymptotes on the graph.

**Q: What is arctan (inverse tangent)?**

A: Arctan (also written tan⁻¹) returns the angle whose tangent is a given value. Unlike arcsin and arccos, arctan accepts any real number as input. It always returns an angle between -90° and 90° (exclusive).

**Q: What is the relationship between tangent and slope?**

A: The tangent of the angle a line makes with the x-axis equals the slope of that line: m = tan(θ). A 45° line has slope tan(45°) = 1. A horizontal line has slope tan(0°) = 0. A vertical line has undefined slope, matching tan(90°) = undefined.

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Source: https://vastcalc.com/calculators/math/tangent
Category: Math
Last updated: 2026-04-21