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