# cosecant

The trigonometric function sec allows to calculate the secant of an angle expressed in radians, degrees, or grades.
cosec(pi/2), returns 1

### Cosec, online calculus

#### Summary :

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

# Cosecant function

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

### Cosecant calculating an angle in radians

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.

### Calculate the cosecant of an angle in degrees

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.

### Calculate the cosecant of an angle in gradians

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.

## Special cosecant values table

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

## Derivative of cosecant

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

## Antiderivative of cosecant

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

## Properties of the cosecant function

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.

#### Syntax :

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

#### Examples :

cosec(pi/2), returns 1

#### Derivative cosecant :

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 cosecant :

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)))

#### Limit cosecant :

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

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

#### Graphic cosecant :

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

#### Property of the function cosecant :

The cosecant function is an odd function.
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