sin(`0`), returns 0

The sin trigonometric function to calculate the sin of an angle in radians, degrees or gradians.

The calculator allows to use most of the **trigonometric functions**, it is possible to calculate the
**sine**,
the cosine
and the tangent
of an angle through the functions of the same name..

The **trigonometric function sine** noted **sin**,
allows to **calculate
the sine of an angle online **, it is possible to use different angular units :
degree, grade and radians wich is the angular unit by default.

- Calculation of the sine
- Special sine values table
- Main properties
- `sin(-x)= -sin(x)`
- `sin(x+2*k*pi)=sin(x)`
- `sin(pi-x)=sin(x)`
- `sin(pi+x)=-sin(x)`
- `sin(pi/2-x)=cos(x)`
- `sin(pi/2+x)=cos(x)`
- Derivative of sine
- Antiderivative of sine
- Properties of the sine function
- Equation with sine

The **sine calculator** allows through the sin function to **calculate**
**online** the **sine** sine of an angle in radians, you must first
select the desired unit by clicking on the options button calculation module.
After that, you can start your calculations.

To **calculate sine online** of `pi/6`, enter
sin(`pi/6`), after calculation, the result
`1/2` is returned.

Note that the sine function is able to recognize some special angles and make the calculations with special associated values in exact form.

To **calculate the sine of an angle** in degrees, you must first select the desired unit
by clicking on the options button calculation module. After that, you can start your calculus.

To calculate sine of 90, enter sin(90), after calculation, the restults 1 is returned.

To calculate the sine of an angle in gradians, you must first select the desired unit by clicking on the options button calculation module. After that, you can start your calculus.

To calculate sine of 50, enter sin(50), after computation, the result `sqrt(2)/2` is returned.

Note that the sine function is able to recognize some special angles and do the calculus with special associated exact values.

The sine admits some special values which the calculator is able to determine in exact forms. Here is a table of
the **commonsine values**:

sin(`2*pi`) | `0` |

sin(`pi`) | `0` |

sin(`pi/2`) | `1` |

sin(`pi/4`) | `sqrt(2)/2` |

sin(`pi/3`) | `sqrt(3)/2` |

sin(`pi/6`) | `1/2` |

sin(`2*pi/3`) | `sqrt(3)/2` |

sin(`3*pi/4`) | `sqrt(2)/2` |

sin(`5*pi/6`) | `1/2` |

sin(`0`) | `0` |

sin(`-2*pi`) | `0` |

sin(`-pi`) | `0` |

sin(`pi/2`) | `-1` |

sin(`-pi/4`) | `-sqrt(2)/2` |

sin(`-pi/3`) | `-sqrt(3)/2` |

sin(`-pi/6`) | `-1/2` |

sin(`-2*pi/3`) | `-sqrt(3)/2` |

sin(`-3*pi/4`) | `-sqrt(2)/2` |

sin(`-5*pi/6`) | `-1/2` |

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The derivative of the sine is equal to cos(x).

The antiderivative of the sine is equal to -cos(x).

The **sine** function is an odd function, for every real x, `sin(-x)=-sin(x)`.
The consequence for the curve representative of the sine function is that it admits the origin of the reference point as point of symmetry.

The calculator has a solver which allows it to solve
equation with sine
of the form **cos(x)=a**.
The calculations to obtain the result are detailed, so it will be possible to solve equations like
`sin(x)=1/2`
or
`2*sin(x)=sqrt(2)`
with the calculation steps.

sin(x), where x is the measure of an angle in degrees, radians, or gradians.

sin(`0`), returns 0

To differentiate function sine online, it is possible to use the derivative calculator which allows the calculation of the derivative of the sine function

The **derivative of sin(x)** is derivative(`sin(x)`)=`cos(x)`

Antiderivative calculator allows to calculate an antiderivative of sine function.

An **antiderivative of sin(x)** is antiderivative(`sin(x)`)=`-cos(x)`

The limit calculator allows the calculation of limits of the sine function.

The **limit of sin(x)** is limit(`sin(x)`)

The **inverse function of sine** is the arcsine function noted arcsin.

The graphing calculator is able to plot sine function in its definition interval.

See also

- Arccosine : arccos. The arccos function allows the calculation of the arc cosine of a number. The arccos function is the inverse functions of the cosine function.
- Arcsine : arcsin. The arcsin function allows the calculation of the arc sine of a number. The arcsin function is the inverse function of the sine function.
- Arctangent : arctan. The arctan function allows the calculation of the arctan of a number. The arctan function is the inverse functions of the tangent function.
- Trigonometric Calculator : simplify_trig. Calculator wich uses trigonometric formula to simplify trigonometric expression.
- Cosine : cos. The cos trigonometric function calculates the cos of an angle in radians, degrees or gradians.
- Cosecant : cosec. The trigonometric function sec allows to calculate the secant of an angle expressed in radians, degrees, or grades.
- Cotangent : cotan. The cotan trigonometric function to calculate the cotan of an angle in radians, degrees or gradians.
- Trigonometric expansion : expand_trigo. The calculator makes it possible to obtain the trigonometric expansion of an expression.
- Trigonometric linearization : linearization_trigo. Calculator that allows to linearize a trigonometric expression.
- Simplify Calculator : simplify. Calculator wich can simplify an algebraic expression online.
- Secant : sec. The trigonometric function sec allows to calculate the secant of an angle expressed in radians, degrees, or grades.
- Sine : sin. The sin trigonometric function to calculate the sin of an angle in radians, degrees or gradians.
- Tangent : tan. The tan trigonometric function to calculate the tan of an angle in radians, degrees or gradians.