Calculate the tangent of any angle in degrees, radians, or gradians. See all 6 trig functions, asymptote warnings, quadrant identification, and a common values table.
The **Tangent Calculator** computes tan(θ) for any angle input in degrees, radians, or gradians. Tangent is the ratio of the opposite side to the adjacent side in a right triangle, or equivalently sin(θ)/cos(θ). It is one of the most used trigonometric functions in mathematics, physics, and engineering.
Beyond the primary tangent value, this calculator displays all six trigonometric functions — sine, cosine, tangent, cosecant, secant, and cotangent — from a single angle input. It identifies the quadrant of the angle, warns when the tangent is undefined (at odd multiples of 90°), and shows the period and reference angle for deeper analysis.
Tangent is unique among the basic trig functions because it has a period of π (180°) rather than 2π, and it is unbounded — approaching positive or negative infinity near its vertical asymptotes. Understanding where tan is positive, negative, zero, or undefined is essential for solving trig equations and graphing.
The tool includes preset buttons for standard angles, a tangent value indicator bar that shows where the result falls relative to common reference values, and a comprehensive table of tangent values from 0° to 360° in 15° increments. Whether you are checking homework, building an engineering model, or reviewing for an exam, this calculator gives you everything you need at a glance.
Tangent Calculator (tan θ) — All Trig Functions & Quadrant Info helps you avoid repetitive setup mistakes when solving trigonometric and coordinate-geometry problems. Instead of recalculating conversions, signs, and edge cases by hand, you can test inputs immediately, inspect intermediate values, and confirm final answers before submitting work or using numbers in downstream calculations. It surfaces key outputs like tan(θ), sin(θ), cos(θ) in one pass.
tan(θ) = sin(θ)/cos(θ) = opposite/adjacent. Period = π (180°). Undefined when cos(θ) = 0 (θ = 90° + n·180°). tan(−θ) = −tan(θ) (odd function).
Result: 1
Using θ=45°, the calculator returns 1. This example mirrors the calculator's live computation flow and is useful for checking manual steps and unit handling.
This calculator is tailored to tangent calculator (tan θ) — all trig functions & quadrant info workflows, including common input modes, unit handling, and special-case behavior. It is designed for fast checking during homework, exam preparation, technical drafting, and coding tasks where trigonometric consistency matters.
Use the primary result together with supporting outputs to verify direction, magnitude, and validity. Cross-check against known identities or geometric constraints, and confirm that angle ranges, sign conventions, and domain restrictions are satisfied before using the numbers elsewhere.
A reliable way to improve is to solve once manually, then verify with the calculator and explain any mismatch. Repeat this on varied examples and edge cases. The built-in preset scenarios for quick trials, comparison tables for side-by-side validation, visual cues that make trends and quadrants easier to read help you build pattern recognition and reduce sign or conversion errors over time.
Tangent is the ratio of the sine to the cosine of an angle: tan(θ) = sin(θ)/cos(θ). In a right triangle, it equals the length of the opposite side divided by the adjacent side.
Tangent is undefined when cos(θ) = 0, which occurs at θ = 90° + n·180° for any integer n (90°, 270°, −90°, …). At these points the tangent graph has vertical asymptotes.
The period of tan(θ) is π radians, or 180°. This means tan(θ + 180°) = tan(θ) for every angle θ.
Tangent is positive in Quadrant I (0°–90°) and Quadrant III (180°–270°), and negative in Quadrant II (90°–180°) and Quadrant IV (270°–360°). Use this as a practical reminder before finalizing the result.
tan(45°) = 1. This is because sin(45°) and cos(45°) are both √2/2, and their ratio is 1.
The slope of a line equals the tangent of the angle it makes with the positive x-axis. A line with slope m makes an angle θ = arctan(m) with the horizontal.