Cotangent Calculator

Cotangent is the reciprocal of tangent. In a right triangle it is the adjacent side divided by the opposite side, and in unit-circle terms it is cosine divided by sine. It is useful in trigonometric identities, slopes, surveying, and problems where an adjacent-to-opposite ratio is more convenient than tangent.

This page accepts an angle in degrees, calculates tangent after converting to radians, takes its reciprocal, and rounds to six decimal places. Cotangent is undefined wherever sine is zero, including integer multiples of 180°.

1. Enter an angle in degrees. Decimal and negative inputs are allowed.
2. Select Calculate. The page converts degrees to radians and evaluates tangent.
3. It checks whether tangent is effectively zero. If so, it reports that cotangent is undefined at this angle; otherwise it divides 1 by tangent and rounds to six places.

The mathematical result repeats every 180°: cot(θ + 180°) = cot(θ). The near-zero check prevents misleading huge values at familiar undefined inputs such as 0° and 180°. Angles extremely close to those points can still have valid cotangents with very large magnitude.

• Entering radians; the form interprets the number as degrees.
• Using opposite divided by adjacent, which is tangent rather than cotangent.
• Assuming cotangent means inverse tangent. Arctangent returns an angle; cotangent is a reciprocal ratio.
• Ignoring the undefined warning at 0°, 180°, or another multiple of 180°.
• Rounding an angle close to an undefined point before calculating.
• Forgetting that cotangent repeats every 180°, rather than every 360° as a smallest positive period.

Is cotangent the same as inverse tangent?

No. Cotangent is 1/tan(θ). Inverse tangent, written arctan or sometimes tan⁻¹, starts with a ratio and returns a principal angle.

When is cotangent undefined?

It is undefined whenever sin(θ) = 0, at integer multiples of 180°. The calculator checks for these near-zero tangent cases and displays an error instead of a numeric result.

Does the calculator use degrees?

Yes. Convert radians to degrees by multiplying by 180/π before entering the angle.

Why is the result very large near 180°?

Sine approaches zero near 180°, and cotangent divides cosine by sine. The ratio grows without bound in magnitude as the angle approaches the undefined point from either side.

What is the period of cotangent?

Cotangent repeats every 180°, or π radians. Adding 180° changes both sine and cosine signs, so their ratio remains the same.

Where does cotangent equal zero?

Cotangent is zero where cosine is zero and sine is nonzero: 90° plus any integer multiple of 180°. The page rounds sufficiently small computed values to zero.

Can cotangent describe a right-triangle side ratio?

Yes. For an acute angle, cotangent is adjacent divided by opposite. If cot(θ) = 2, the adjacent leg is twice the opposite leg for that angle, regardless of the triangle’s overall scale.

Why can cotangent be negative?

On the unit circle, cotangent is cosine divided by sine. The quotient is negative when those coordinates have opposite signs, which occurs in quadrants II and IV. A negative result is therefore expected for many valid angles and does not indicate a calculation failure.

How should I round a cotangent result?

Keep the six-place result or more precision until the final step of a longer calculation, then round to the precision justified by the angle or measurements. Near undefined points, extra digits in the angle matter greatly.

• OpenStax Precalculus 2e — Unit-circle functions
• OpenStax Precalculus 2e — Other trigonometric functions