Cotangent Calculator
Calculate the cotangent of any angle in degrees or radians.
Calculator
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Table of Contents
Concept
What is Cotangent?
The cotangent function is one of the primary trigonometric functions. In a right triangle, the cotangent of an angle is the ratio of the length of the adjacent side to the length of the opposite side.
Definition:
In a right triangle, cot(θ) = adjacent/opposite
Formula
Cotangent Formula
The cotangent function can be calculated using the following formula:
Formula:
cot(θ) = adjacent/opposite = cos(θ)/sin(θ) = 1/tan(θ)
Values
Common Cotangent Values
Special Angles
- cot(0°) = undefined
- cot(30°) = 1.7321
- cot(45°) = 1
- cot(60°) = 0.5774
- cot(90°) = 0
Properties
- Range: (-∞, ∞)
- Period: 180° or π radians
- Odd function: cot(-θ) = -cot(θ)
- cot(θ + 180°) = cot(θ)
Applications
Applications of Cotangent
Physics Wave Motion
Cotangent functions are used to model wave motion, including sound waves, light waves, and water waves.
Engineering Signal Processing
Cotangent functions are fundamental in signal processing, electrical engineering, and communications systems.
Navigation GPS and Location
Cotangent functions are used in GPS systems and navigation to calculate distances and positions.
Tools
Trigonometry Calculators
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