# Sine Calculator

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

> The sine calculator finds sin 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

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

## Formula

```
sin α = opposite / hypotenuse = y-coordinate on the unit circle
Range: [−1, 1] · Domain: all real numbers · Period: 2π (360°)
```

## Explanation

The sine of an angle is the ratio of the side opposite the angle to the hypotenuse of a right triangle; on the unit circle it is the y-coordinate of the point at angle α. Sine waves describe sound, light, alternating current, tides and every kind of oscillation.

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

## Key terms

- **Sine**: sin α = opposite / hypotenuse = y-coordinate on the unit circle.
- **Exact value**: A value written with integers and square roots instead of decimals.

## FAQ

**What is sin 30°?**
Exactly 1/2.

**What is sin 90°?**
1, the largest value sine takes.

**Is sine positive in the second quadrant?**
Yes – sine is positive in quadrants I and II and negative in III and IV.

**How do I get the angle back from a sine value?**
Use arcsin; remember that a second angle 180° − α has the same sine.


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