Tangent Calculator
Calculate tangent values
Frequently Asked Questions
What is the tangent function?
Tangent is a trigonometric ratio: tan(θ) = opposite / adjacent = sin(θ) / cos(θ). In a right triangle with angle 45°: tan(45°) = 1. The calculator works in both degrees and radians.
What is the tangent line to a curve?
A tangent line touches a curve at exactly one point and has the same slope as the curve at that point. The slope equals the derivative: slope = f'(x₀). The tangent line equation is y - f(x₀) = f'(x₀)(x - x₀).
Where is tangent undefined?
Tangent is undefined at 90° (π/2) and 270° (3π/2), and generally at (90° + 180°n) for any integer n. At these angles, cosine equals zero, making the ratio sin/cos undefined. The graph has vertical asymptotes at these points.
What is the inverse tangent (arctan)?
Arctan (tan⁻¹) finds the angle whose tangent is a given value. arctan(1) = 45° because tan(45°) = 1. The range of arctan is (-90°, 90°) or (-π/2, π/2). The calculator computes both tan and arctan.
How is tangent used in real-world applications?
Tangent calculates slopes and angles of elevation. If a building is 50m away and you look up at 60°: height = 50 × tan(60°) = 86.6m. It is used in surveying, navigation, engineering, and physics.