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Math

Cotangent Calculator.

Calculates the cotangent of an angle in degrees or radians.

Results update live as you type.
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Your inputs

How it works

  1. 1

    Enter the angle in degrees.

  2. 2

    The calculator converts degrees to radians.

  3. 3

    It computes the tangent of the angle.

  4. 4

    It takes the reciprocal to get the cotangent.

1 / tan(angle * pi / 180)

Frequently asked questions

What is cotangent?

Cotangent is the reciprocal of tangent: cot(x) = 1/tan(x).

Why is cotangent undefined at 0° and 180°?

Because tangent is zero at those angles, so the reciprocal is undefined.

Can I input angles in radians?

This calculator uses degrees. For radians, multiply by 180/π.

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Results

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Cotangent

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How it works

Calculates the cotangent of an angle in degrees or radians.

  1. Enter the angle in degrees.
  2. The calculator converts degrees to radians.
  3. It computes the tangent of the angle.
  4. It takes the reciprocal to get the cotangent.

Formulas

The math behind this calculator, written out so you can verify the result.

Cotangent definition

cot(θ) = 1 / tan(θ)

Cotangent is the reciprocal of the tangent function.

Example:

Input: θ = 45°

Calculation: 1 / tan(45°) = 1 / 1

Result: 1

Real-world use cases

Where this calculation shows up in everyday life.

Trigonometry problems

Solve right triangles and trigonometric equations.

Example: Finding the slope of a line given an angle.

Physics applications

Used in wave motion and oscillations.

Example: Calculating phase angles.

Engineering calculations

Useful in structural analysis and design.

Example: Determining forces on inclined planes.

Tips and common mistakes

Tips

  • Remember cot(θ) = cos(θ)/sin(θ).
  • Use a calculator with degree mode for quick checks.
  • Cotangent is periodic with period 180°.
  • For angles where tan is zero, cot is undefined.

Common Mistakes to Avoid

  • Forgetting to convert degrees to radians in manual calculations.
  • Confusing cotangent with arctangent.
  • Using the calculator in radian mode when entering degrees.

Assumptions and limitations

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.