Cosecant Calculator
Calculate the cosecant (csc) of an angle in different units.
Graph
Cosecant Function
The cosecant function is defined as:
\[ \csc(\theta) = \frac{1}{\sin(\theta)} \]
Properties:
- Domain: All real numbers except nπ (where n is an integer)
- Range: (-∞, -1] ∪ [1, ∞)
- Period: 2π
- \(\csc(-\theta) = -\csc(\theta)\)
- \(\csc(\theta + 2\pi) = \csc(\theta)\)
Common Values:
- \(\csc(0)\) is undefined
- \(\csc(\frac{\pi}{2}) = 1\)
- \(\csc(\pi)\) is undefined
- \(\csc(\frac{3\pi}{2}) = -1\)
- \(\csc(\frac{\pi}{6}) = 2\)
Applications:
- Trigonometry
- Physics (wave motion)
- Engineering (signal processing)
- Navigation
- Computer graphics
Geometric Interpretation:
- Reciprocal of sine
- Ratio of hypotenuse to opposite side
- Vertical asymptotes at nπ
- Symmetrical about origin
- Periodic with period 2π