cosec(`pi/2`), returns 1

The trigonometric function sec allows to calculate the secant of an angle expressed in radians, degrees, or grades.

The cosecant trigonometric function noted cosec, allows the calculation of the cosecant of an angle, it is possible to use different angular units: the radian which is the default angular unit, the degree or the grade. The cosecant function is equal to the inverse of the sine function, `cosec(x)=1/sin(x)`

- Compute the cosecant
- Special cosecant values table
- Derivative of cosecant
- Antiderivative of cosecant
- Properties of the cosecant function

The **cosecant calculator** allows through the cosec function to **calculate**
**online** the **cosecant** cosecant 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 cosecant online** of `pi/6`, enter
cosec(`pi/6`), after calculation, the result
is returned.

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

To **calculate the cosecant 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 cosecant of 45, enter cosec(45), after calculation, the restults is returned.

To calculate the cosecant 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 cosecant of 50, enter cosec(50), after computation, the result is returned.

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

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

Value | cosec | Result |
---|---|---|

`pi/6` | cosec(`pi/6`) | `2` |

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

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

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

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

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

`5*pi/6` | cosec(`5*pi/6`) | `2` |

The derivative of the cosecant is equal to `-cos(x)/sin(x)^2``=``-"cotan"(x)*"cosec"(x)`.

The antiderivative of the cosecant is equal to `1/2*ln((1-cos(x))/(1+cos(x)))`.

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

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

cosec(`pi/2`), returns 1

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

The **derivative of cosec(x)** is derivative(`"cosec"(x)`)=`-cos(x)/sin(x)^2`

Antiderivative calculator allows to calculate an antiderivative of cosecant function.

An **antiderivative of cosec(x)** is antiderivative(`"cosec"(x)`)=`1/2*ln((1-cos(x))/(1+cos(x)))`

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

The **limit of cosec(x)** is limit(`"cosec"(x)`)

The graphing calculator is able to plot cosecant 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.