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Calculate the cosecant of any angle. Cosecant is the reciprocal of sine: csc(θ) = 1/sin(θ).
| Degrees | Radians | Exact Value | Decimal |
|---|---|---|---|
| 0° | 0 | undefined | — |
| 30° | π/6 | 2 | 2.0000 |
| 45° | π/4 | √2 | 1.4142 |
| 60° | π/3 | 2√3/3 | 1.1547 |
| 90° | π/2 | 1 | 1.0000 |
| 120° | 2π/3 | 2√3/3 | 1.1547 |
| 135° | 3π/4 | √2 | 1.4142 |
| 150° | 5π/6 | 2 | 2.0000 |
| 180° | π | undefined | — |
| 270° | 3π/2 | -1 | -1.0000 |
All θ except 0°, 180°, 360°, ...
Where sin(θ) ≠ 0
(-∞, -1] ∪ [1, ∞)
|csc(θ)| ≥ 1
2π radians (360°)
csc(θ + 2π) = csc(θ)
Odd function: csc(-θ) = -csc(θ)
Origin symmetry
Cosecant is the reciprocal of sine. It equals 1 divided by the sine of the angle, or in a right triangle, hypotenuse divided by opposite side.
Since |sin(θ)| ≤ 1, and csc = 1/sin, the absolute value of cosecant must be ≥ 1 (except at undefined points).
Cosecant is undefined when sin(θ) = 0, which occurs at 0°, 180°, 360°, and all integer multiples of 180°.