Why is tan(90°) undefined?

tan(90°) is undefined because tan(θ) = sin(θ)/cos(θ), and cos(90°) = 0. Division by zero is undefined. Similarly, tan(270°) and other angles where cos(θ) = 0 are also undefined.

How to convert tan between rad/deg?

The tangent function works the same way in both radians and degrees. Just make sure your input angle is in the correct unit. Our calculator automatically handles the conversion when you switch modes.

📐 Tangent Calculator (tan x)

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

Tangent Calculator

Angle

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.

Related Calculators

📐

Trigonometry Calculator

Free trigonometry calculator for sin, cos, tan, and inverse trig functions. Convert degrees/radians, explore graphs, unit circle values, and trig tables. Fast, accurate, and easy to use.

Try it now

📐

Sine Calculator (sin x)

Instantly compute sin(x) in degrees or radians. Includes graph insights, common values, and quick examples.

Try it now

📐

Cosine Calculator (cos x)

Calculate cos(x) instantly in degrees or radians. Includes cosine properties and common angle values.

Try it now

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