# Secant Calculator

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

> The secant calculator finds sec 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

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

## Formula

```
sec α = 1 / cos α = hypotenuse / adjacent
Range: (−∞, −1] ∪ [1, ∞) · Domain: α ≠ 90° + k·180° · Period: 2π (360°)
```

## Explanation

The secant is the reciprocal of the cosine: hypotenuse divided by adjacent side. The identity 1 + tan²α = sec²α makes it a regular guest in calculus, and it gives slant lengths from horizontal distances.

### How to use the Secant 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 sec 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 — **sec(α) = 1.154700538**; sin(α) = 1/2 ≈ 0.5; cos(α) = √3/2 ≈ 0.8660254038; tan(α) = √3/3 ≈ 0.5773502692; csc(α) = 2; cot(α) = 1.732050808.

## Key terms

- **Secant**: sec α = 1 / cos α = hypotenuse / adjacent.
- **Exact value**: A value written with integers and square roots instead of decimals.

## FAQ

**What is sec 60°?**
2, because cos 60° = 1/2.

**When is secant undefined?**
When cos α = 0: at 90°, 270° and so on.

**Is secant even?**
Yes, like cosine: sec(−α) = sec α.

**What identity links secant and tangent?**
1 + tan²α = sec²α.


## 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 – Secant](https://mathworld.wolfram.com/Secant.html)