Calculate the tangent of any angle in degrees or radians, with pole detection.
The tangent function returns the ratio of the opposite side to the adjacent side (equivalently sin/cos). It is undefined at 90° + k·180° where cos = 0. This calculator detects those poles and returns a descriptive message rather than an error value.
Tangent definition
tan θ = sin θ / cos θ = opposite / adjacent
tan(θ) = sin(θ)/cos(θ). At 90°, cos = 0, so we divide by zero. The function has vertical asymptotes at all odd multiples of 90°.
tan(45°) = 1, because sin(45°) = cos(45°) ≈ 0.7071, and their ratio is exactly 1.