Compute the tangent of an angle expressed in radians.
TAN(expr)## Overview Returns the tangent of an angle supplied in radians. Tangent appears in slope calculations, projective geometry, field-of-view formulas, and in any trigonometric identity where sin/cos must be combined into a single ratio. Unlike SIN and COS, the tangent function is unbounded. It grows toward positive infinity as the angle approaches pi/2 from below, and toward negative infinity from above. Because the argument reduction is never exact, TAN at the theoretical singularity returns a very large finite number rather than producing an error. ## Behavior - Accepts any finite DOUBLE value. - Returns a DOUBLE that is unbounded. The output domain is the full real line. - Returns NULL if the argument is NULL. - Returns NaN for NaN input. Returns a very large magnitude near odd multiples of pi/2 rather than infinity. - Is deterministic and matches SIN(x) / COS(x) to within one ULP for normal inputs. ## Numeric precision - Evaluated using IEEE 754 double-precision tan. Accurate to within one ULP in the stable range. - Near odd multiples of pi/2, small input changes cause large output swings. Use TAN cautiously as a predicate on continuous data. - As with SIN and COS, argument magnitudes above 1e15 lose meaningful trigonometric precision. ## Compatibility - Conforms to the SQL standard. - Matches the behavior of IEEE 754 tan in typical mathematical libraries.
| Name | Type | Description |
|---|---|---|
expr | Specifies the angle in radians whose tangent is returned. Accepts any finite DOUBLE value except odd multiples of pi/2 (where the tangent is undefined). |
-- Basic literal
SELECT TAN(0);
-- Result: 0.0-- Tangent of pi/4 evaluates to 1
SELECT TAN(PI() / 4);
-- Result: 0.9999999999999999-- Convert degrees to radians first
SELECT TAN(RADIANS(45));
-- Result: 0.9999999999999999-- Identity: TAN(x) = SIN(x) / COS(x)
SELECT TAN(0.5), SIN(0.5) / COS(0.5);
-- Result: 0.5463024898437905, 0.5463024898437905-- Near-singularity: TAN(PI()/2) returns a very large (not infinite) value
SELECT TAN(PI() / 2);
-- Result: 1.633123935319537E16-- Column use: slope of a line from angle
SELECT segment_id, TAN(RADIANS(incline_deg)) AS slope
FROM roads.catalog.segments;