Cot
Calculate the cotangent of any angle in degrees using the formula cot(theta) = 1 / tan(theta). Free online trigonometry calculator with step-by-step results, instant output, and support for all real angles including acute, obtuse, and reflex angles.
About This Calculator
The cotangent (cot) calculator is a free online trigonometry tool that computes the cotangent of any angle entered in degrees. Cotangent is one of the six fundamental trigonometric functions and is defined as the reciprocal of tangent: cot(theta) = 1 / tan(theta). In a right triangle, cotangent represents the ratio of the adjacent side to the opposite side.
How the cotangent formula works
When you enter an angle in degrees, the calculator first converts it to radians by multiplying by pi / 180. It then computes tan(theta) using the standard Math.tan function and returns its reciprocal. The result is displayed with up to 6 decimal places. If tan(theta) equals zero (at multiples of 180 deg), the cotangent is undefined and the calculator returns no output for that angle.
Who uses cotangent calculations
Cotangent is widely used by students learning trigonometry and precalculus, engineers working with angles and slopes, physicists analyzing wave motion and periodic phenomena, surveyors calculating elevations and distances, and computer graphics developers working with 3D rotations and lighting models. The cotangent function is also encountered in calculus when integrating trigonometric expressions and in electrical engineering for analyzing AC circuits and impedance.
Key properties
Cotangent is an odd, periodic function with period 180 deg (pi radians). Its domain excludes integer multiples of 180 deg where tan(theta) = 0. The range of cotangent spans all real numbers (-∞ to +∞). Key values include: cot(45 deg) = 1, cot(60 deg) = 0.57735, cot(30 deg) = 1.73205, and cot(90 deg) = 0. The function decreases monotonically over each interval where it is defined.
Tips for accurate results
Enter angles as decimal numbers (e.g. 45.5) for precise results. The calculator accepts any real number including negative angles and angles larger than 360 deg. Remember that cot(theta) = cos(theta) / sin(theta) as an alternative definition. Use the share button to save or share your calculation via the page URL, which preserves your input angle for easy reference.
Frequently Asked Questions
What is cotangent and how is it calculated?
Cotangent (cot) is the reciprocal of tangent: cot(theta) = 1 / tan(theta) = adjacent side / opposite side in a right triangle. This calculator converts the input angle from degrees to radians, computes tan(theta), then takes its reciprocal to return the cotangent value.
What is the difference between cot and arctan?
Cotangent (cot) is the reciprocal of tangent: cot(theta) = 1 / tan(theta) and takes an angle as input. Arctan (tan⁻¹) is the inverse of tangent: it takes a ratio as input and returns the angle whose tangent equals that ratio. They are fundamentally different operations.
What is the cot of 0 degrees?
The cotangent of 0 degrees is undefined (infinite) because tan(0 deg) = 0 and cot(0 deg) = 1 / 0, which approaches +∞. The calculator returns undefined for angles where tan(theta) = 0 (multiples of 180 deg).
What is the cot of 45 degrees?
The cotangent of 45 degrees is exactly 1, because tan(45 deg) = 1 and cot(45 deg) = 1 / 1 = 1.
What is the cot of 60 degrees?
The cotangent of 60 degrees is 1 / sqrt3 ≈ 0.57735. This follows from tan(60 deg) = sqrt3, so cot(60 deg) = 1 / sqrt3.
Where is cotangent used in real-world applications?
Cotangent is used in surveying and navigation (slope calculations), physics (wave functions and oscillations), engineering (stress analysis), computer graphics (lighting and rotation calculations), and electrical engineering (AC circuit analysis). It is also essential in calculus for integrating and differentiating trigonometric functions.
Can I enter negative angles?
Yes, this calculator accepts negative angles. Since cotangent is an odd function, cot(-theta) = -cot(theta). For example, cot(-45 deg) = -1.
How do you convert degrees to radians for cot?
To convert degrees to radians, multiply the angle in degrees by pi / 180. This calculator performs the conversion internally: it first converts degrees to radians, then computes tan(theta), and finally returns 1 / tan(theta).