Cotangent Calculator
Calculate the cotangent (cot) of an angle in different units.
Graph
Cotangent Function
The cotangent function is defined as:
\[ \cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)} = \frac{1}{\tan(\theta)} \]
Properties:
- Domain: All real numbers except nπ (where n is an integer)
- Range: (-∞, ∞)
- Period: π
- \(\cot(-\theta) = -\cot(\theta)\)
- \(\cot(\theta + \pi) = \cot(\theta)\)
Common Values:
- \(\cot(0)\) is undefined
- \(\cot(\frac{\pi}{2}) = 0\)
- \(\cot(\pi)\) is undefined
- \(\cot(\frac{3\pi}{2}) = 0\)
- \(\cot(\frac{\pi}{6}) = \sqrt{3}\)
- \(\cot(\frac{\pi}{4}) = 1\)
- \(\cot(\frac{\pi}{3}) = \frac{1}{\sqrt{3}}\)
Applications:
- Trigonometry
- Physics (wave motion)
- Engineering (signal processing)
- Navigation
- Computer graphics
Geometric Interpretation:
- Ratio of adjacent to opposite side in a right triangle
- Reciprocal of tangent
- Vertical asymptotes at nπ
- Periodic with period π
- Odd function (symmetric about origin)