# Cosecant Calculator

URL: https://speedycalculator.com/calculators/math/csc/
Last updated: 2026-10-30

> The cosecant calculator finds csc α for any angle in degrees, radians or multiples of π, with the exact value for multiples of 15° and the five other trigonometric functions of the same angle.

## Inputs

- Angle unit
- Angle α

## Results

- csc(α)
- sin(α)
- cos(α)
- tan(α)
- sec(α)
- cot(α)

## Formula

```
csc α = 1 / sin α = hypotenuse / opposite
Range: (−∞, −1] ∪ [1, ∞) · Domain: α ≠ k·180° · Period: 2π (360°)
```

## Explanation

The cosecant is the reciprocal of the sine: hypotenuse divided by opposite side. It appears in integrals, in the law of sines written as a/sin A = 2R, and when solving triangles for a hypotenuse.

### How to use the Cosecant Calculator

- **Angle unit**
- **Angle α**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

Enter the angle and pick its unit. The angle is converted to radians and csc is evaluated; for multiples of 15° the exact value with square roots is shown as well (for example √3/2). Where the function is undefined, the calculator says so instead of printing a huge number.

## Worked example

Inputs — Angle unit: Degrees (°); Angle α: 30.

Results — **csc(α) = 2**; sin(α) = 1/2 ≈ 0.5; cos(α) = √3/2 ≈ 0.8660254038; tan(α) = √3/3 ≈ 0.5773502692; sec(α) = 1.154700538; cot(α) = 1.732050808.

## Key terms

- **Cosecant**: csc α = 1 / sin α = hypotenuse / opposite.
- **Exact value**: A value written with integers and square roots instead of decimals.

## FAQ

**What is csc 30°?**
2, because sin 30° = 1/2.

**When is cosecant undefined?**
When sin α = 0: at 0°, 180°, 360° and so on.

**Is cosecant the same as arcsin?**
No – csc is 1/sin, arcsin is the inverse function.

**Can csc be between −1 and 1?**
Never – |csc α| ≥ 1.


## Sources

- [OpenStax – Algebra and Trigonometry 2e](https://openstax.org/details/books/algebra-and-trigonometry-2e)
- [OpenStax – Precalculus 2e](https://openstax.org/details/books/precalculus-2e)
- [Wolfram MathWorld – Cosecant](https://mathworld.wolfram.com/Cosecant.html)