# Sine Calculator

A sine calculator is a useful online tool or software program that allows you to calculate the sine value of an angle quickly and accurately. It simplifies the process of evaluating sine values for various angles, whether they are given in radians or degrees.

## Sine expression calculator

A sine expression calculator is a tool or software program that allows you to evaluate and simplify mathematical expressions involving sine functions. It can handle more complex calculations beyond simple angle-based sine values.

## Inverse sine calculator

An inverse sine calculator, also known as an arcsine calculator or sin⁻¹ calculator, is a tool that allows you to find the angle (in radians or degrees) whose sine value is known. In other words, it helps you determine the angle from its corresponding sine value.

## What is Sine

Sine is a mathematical function that relates the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse. In simpler terms, sine is defined as the ratio of the length of the side opposite to a given angle to the length of the hypotenuse in a right triangle. It is denoted as sin(x), where x represents the angle.

The sine function takes an angle (in radians or degrees) as input and returns a value between -1 and 1. The value indicates the ratio between the vertical displacement and the hypotenuse length in the right triangle.

The sine function is widely used in various fields such as mathematics, physics, engineering, and computer science. It plays a fundamental role in trigonometry, waveforms, periodic functions, and many other applications involving angles and oscillatory phenomena.

## Sine Formula

The sine formula relates the angles and sides of a right triangle. In a right triangle, if we denote one of the acute angles as θ, the lengths of the sides opposite, adjacent, and hypotenuse as opposite side (opposite), adjacent side (adjacent), and hypotenuse (hypotenuse) respectively, then the sine formula is defined as:

sin(θ) = opposite / hypotenuse

Alternatively, we can use the Pythagorean theorem to express the sine formula as:

sin(θ) = sqrt(1 - cos^2(θ))

where cos(θ) denotes the cosine of the angle θ.

These formulas allow us to calculate the sine of an angle when we know the lengths of the sides of a right triangle, or vice versa, to find the length of a side when the angle and one side length are known. The sine formula is fundamental in trigonometry and has various applications in fields like geometry, physics, engineering, and wave analysis.

## Sine table

x (deg) |
x (rad) |
sin(x) |
---|---|---|

-90° | -π/2 | -1 |

-60° | -π/3 | -√3/2 |

-45° | -π/4 | -√2/2 |

-30° | -π/6 | -1/2 |

0° | 0 | 0 |

30° | π/6 | 1/2 |

45° | π/4 | √2/2 |

60° | π/3 | √3/2 |

90° | π/2 | 1 |