Cotangent Calculator – Guide & Formulas
Calculate the cotangent (cot) of any angle instantly. Enter an angle in degrees or radians to find cot(x) with step-by-step results.
The Cotangent Calculator computes the cotangent of any angle. Enter an angle in degrees or radians and instantly receive cot(x) = 1/tan(x) with the tangent value, step-by-step breakdown, and a reference table of common cotangent values.
Key Takeaway
Use the free Cotangent Calculator to calculate the cotangent (cot) of any angle instantly. enter an angle in degrees or radians to find cot(x) with step-by-step results. Get instant results with step-by-step explanations.
How to Use the Cotangent Calculator
- Enter an angle value in the input field.
- Select degrees or radians as the angle unit.
- The calculator instantly computes the cotangent result.
- Review the tangent value, cotangent result, and step-by-step explanation.
The Formula
Variable Definitions
- cot(θ): The cotangent of angle θ: the reciprocal of tangent
- θ: The input angle in degrees or radians
- tan(θ): The tangent of angle θ: opposite/adjacent
Example: Cotangent of 45°
Find cot(45°).
- Step 1: First compute tan(45°) = 1.
- Step 2: Apply the formula: cot(45°) = 1 / tan(45°) = 1 / 1.
- Step 3: Therefore cot(45°) = 1.
- Step 4: Verify: tan(45°) × cot(45°) = 1 × 1 = 1 ✓
Frequently Asked Questions
What is cotangent?
Cotangent (cot) is the reciprocal of the tangent function. For any angle θ, cot(θ) = 1/tan(θ) = cos(θ)/sin(θ). In a right triangle, it is the ratio of the adjacent side to the opposite side.
What is the domain of cotangent?
The domain of cot(θ) is all real numbers except where sin(θ) = 0, which occurs at θ = nπ (0°, 180°, 360°, etc.). At these points, cot(θ) is undefined.
What is the range of cotangent?
The range of cot(θ) is all real numbers (-∞, +∞). Unlike cosecant and secant, cotangent can take any real value.
What is cot(45°)?
cot(45°) = 1/tan(45°) = 1/1 = 1. Since tan(45°) = 1, the cotangent at 45° is also 1.
What is cot(0°)?
cot(0°) is undefined because tan(0°) = 0, and dividing by zero is undefined. The cotangent function has a vertical asymptote at 0°.
What is cot(90°)?
cot(90°) = 1/tan(90°). Since tan(90°) is undefined (approaches ∞), cot(90°) = 0.
How is cotangent related to tangent?
Cotangent is the reciprocal of tangent: cot(θ) = 1/tan(θ). Equivalently, tan(θ) = 1/cot(θ). They are inverse multiplicative pairs.
What is the cofunction of cotangent?
The cofunction of cotangent is tangent (tan). The identity is cot(θ) = tan(90° - θ). For example, cot(30°) = tan(60°) = √3.
How do I graph cotangent?
The graph of cot(θ) has vertical asymptotes wherever sin(θ) = 0 (at 0°, 180°, 360°, etc.). Between consecutive asymptotes, the graph decreases from +∞ to -∞.
What are common cotangent values?
Common values: cot(30°) = √3 ≈ 1.732, cot(45°) = 1, cot(60°) = 1/√3 ≈ 0.577, cot(90°) = 0. Undefined at 0°, 180°, 360°.