Calculate the cotangent of any angle in degrees or radians. Identifies undefined points, exact values for special angles, and reciprocal trig.
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Cotangent is the reciprocal trigonometric function of tangent. In a right triangle, cot(θ) is the ratio of the adjacent leg to the opposite leg: cot(θ) = Adjacent / Opposite = cos(θ) / sin(θ) = 1 / tan(θ).
\cot(\theta) = \frac{\text{Adjacent}}{\text{Opposite}} = \frac{1}{\tan(\theta)} = \frac{\cos(\theta)}{\sin(\theta)}Cotangent is undefined whenever sin(θ) = 0, which occurs at integer multiples of 180° (0°, ±180°, ±360°, etc.).
Scenario: Calculate cot(30°)
Given: θ = 30°
cos(30°) = √3 / 2, sin(30°) = 1 / 2
cot(30°) = cos(30°) / sin(30°) = (√3/2) / (1/2) = √3 ≈ 1.732051
At 0°, sin(0°) = 0. Because cot(θ) = cos(θ) / sin(θ), evaluating cot(0°) requires dividing by zero (1 / 0), which is undefined.
They are reciprocals: cot(θ) = 1 / tan(θ) and tan(θ) = 1 / cot(θ). They are also cofunctions: cot(θ) = tan(90° - θ).
cot(30°) = √3, cot(45°) = 1, cot(60°) = √3/3 ≈ 0.577, cot(90°) = 0.
Domain: all real numbers except θ = kπ (k integer). Range: all real numbers (-∞, +∞).
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