Cotangent Calculator

Calculate cotangent (cot) values for angles in degrees and radians with exact values for special angles

Calculate Cotangent

Angle

Enter the angle for which you want to calculate the cotangent

Common Angles

Cotangent Result

Undefined

Cotangent Value

Exact: ∞ (undefined)

Quadrant

0.00° = 0.0000 rad

Formula: cot(x) = cos(x) / sin(x) = 1 / tan(x)

Domain: All real numbers except x = kπ where k is an integer

Range: All real numbers (-∞, ∞)

Quadrant 1 Properties

• Cotangent is positive

• Angle range: 0° to 90° (0 to π/2 rad)

• All trigonometric functions are positive

Related Trigonometric Values

sin(0°)

0.000000

cos(0°)

1.000000

tan(0°)

0.000000

sec(0°)

1.000000

csc(0°)

Undefined

cot(0°)

Undefined

Example Calculation

Calculate cot(60°)

Step 1: Convert to radians: 60° = π/3 radians

Step 2: Find sin(60°) = √3/2 and cos(60°) = 1/2

Step 3: Apply formula: cot(60°) = cos(60°) / sin(60°)

Step 4: cot(60°) = (1/2) / (√3/2) = 1/√3 = √3/3

Special Angle Values

cot(0°) = ∞ (undefined)

cot(30°) = √3

cot(45°) = 1

cot(60°) = √3/3

cot(90°) = 0

cot(180°) = ∞ (undefined)

Cotangent Properties

•

Periodic with period π (180°)

•

Undefined at multiples of π (180°)

•

Odd function: cot(-x) = -cot(x)

•

Range: all real numbers

Unit Circle Reference

0° (0 rad)∞

30° (π/6)√3

45° (π/4)1

60° (π/3)√3/3

90° (π/2)0

Quick Tips

✓

Cotangent is the reciprocal of tangent

✓

Positive in quadrants I and III

✓

Negative in quadrants II and IV

✓

Equal to cos(x)/sin(x)

Understanding the Cotangent Function

What is Cotangent?

The cotangent (cot) is one of the six fundamental trigonometric functions. In a right triangle, it represents the ratio of the adjacent side to the opposite side. For a unit circle, cotangent is defined as the ratio of the x-coordinate to the y-coordinate.