cotangent calculator

What is cotangent?

Cotangent is one of the six primary trigonometric functions. For an angle θ, cotangent is written as cot(θ) and defined as:

cot(θ) = cos(θ) / sin(θ) = 1 / tan(θ)

In a right triangle, cotangent can also be interpreted as adjacent side divided by opposite side. In coordinate geometry and calculus, cotangent shows up in periodic behavior, wave analysis, and many engineering applications.

How to use this cotangent calculator

• Enter an angle value in the input field.
• Select whether your angle is in degrees or radians.
• Choose how many decimal places you want in the result.
• Click Calculate cot(θ) to see the answer instantly.

If your unit is radians, you can enter friendly expressions like pi/4, 3*pi/2, or 2*pi.

Important domain rule (undefined values)

Cotangent is undefined whenever sin(θ) = 0. That means:

• In radians: at θ = nπ for any integer n
• In degrees: at θ = n × 180° for any integer n

At those angles, you are dividing by zero, so the calculator will return an undefined warning instead of a number.

Quick reference values

Degrees

• cot(30°) = √3 ≈ 1.732051
• cot(45°) = 1
• cot(60°) = 1/√3 ≈ 0.577350
• cot(90°) = 0

Radians

• cot(π/6) = √3
• cot(π/4) = 1
• cot(π/3) = 1/√3
• cot(π/2) = 0

Degrees vs radians: avoid common mistakes

One of the most common trig errors is a unit mismatch. A value like 45 means very different things:

• 45 degrees is a standard acute angle.
• 45 radians is a much larger angle after wrapping around the circle several times.

Always confirm your unit setting before calculating cotangent. This calculator keeps units explicit to help prevent that mistake.

Where cotangent is used

Cotangent appears in many math and science contexts, including:

• Trigonometric identities and equation solving
• Signal processing and phase analysis
• Physics models with periodic motion
• Geometry and coordinate transforms
• Calculus, especially derivatives and integrals involving trig functions

Final note

A reliable cotangent calculator should do more than compute a number—it should also handle undefined angles, unit conversion, and precision clearly. Use this tool for homework checks, quick engineering estimates, or trigonometry practice.