Cotangent Calculator
Calculate cotangent and inverse cotangent values with step-by-step solutions
📐 Cotangent Calculator
Formula
cot(θ) = 1/tan(θ) = cos(θ)/sin(θ)
Where:
- θ =Angle in radians or degrees
- cot(θ) =Cotangent value (ratio of adjacent to opposite)
- arccot =Inverse cotangent function
About Cotangent
The cotangent function is one of the six primary trigonometric functions, representing the ratio of the adjacent side to the opposite side in a right triangle, or the reciprocal of tangent.
Key Properties:
- • Range: All real numbers (-∞ to +∞)
- • Period: π radians (180°)
- • Vertical asymptotes at multiples of π
- • cot(π/2) = 0, cot(π/4) = 1, cot(0) = undefined
Common Values:
- • cot(30°) = √3 ≈ 1.732
- • cot(45°) = 1
- • cot(60°) = 1/√3 ≈ 0.577
- • cot(90°) = 0
Relationship to Other Functions:
- • cot(θ) = 1/tan(θ)
- • cot(θ) = cos(θ)/sin(θ)
- • cot²(θ) + 1 = csc²(θ)
Applications:
- • Engineering slope and grade calculations
- • Physics wave analysis and oscillations
- • Computer graphics and 3D modeling
- • Navigation and surveying applications
Tips
- Enter the dimensions in the same unit for consistency.
- Results update automatically as you type.
- Use the unit selector to convert between different measurement systems.