📐 Tangent Calculator (tan x)

Compute tan(x) and highlight undefined positions automatically. Degree/radian support included.

Tangent Calculator

tan(x) =

The tangent function is the ratio of sine to cosine: tan(x) = sin(x)/cos(x). It represents the ratio of the opposite side to the adjacent side in a right triangle. Tangent is undefined when cos(x) = 0, which occurs at 90°, 270°, and their coterminal angles.

Quick Examples

Common tangent values you might encounter.

tan(0°) = 0
The tangent of 0 degrees is 0.
tan(45°) = 1
The tangent of 45 degrees is 1.
tan(60°) = √3 ≈ 1.732
The tangent of 60 degrees is √3.
tan(90°) = Undefined
The tangent of 90 degrees is undefined (division by zero).

Use Cases

Common applications of the tangent function.

📐

Triangle Solving

  • Finding side ratios in right triangles
  • Calculating slopes and angles
  • Solving geometry problems
🏗️

Engineering

  • Calculating slopes and gradients
  • Structural analysis
  • Surveying and navigation

Frequently Asked Questions

Common questions about the tangent function.

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Last updated: 2025-10-21 — Compiled and reviewed by Calvin (Math Research, FreeCalculators.app)