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

Secant function

The secant trigonometric function noted sec, allows the calculation of the secant 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 secant function is equal to the inverse of the cosine function, `sec(x)=1/cos(x)`

Compute the secant

Secant calculating an angle in radians

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

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

Calculate the secant of an angle in degrees

To calculate the secant 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 secant of 45, enter sec(45), after calculation, the restults is returned.

Calculate the secant of an angle in gradians

To calculate the secant 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 secant of 50, enter sec(50), after computation, the result is returned.

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

Special secant values table

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

Value	sec	Result
0	sec(`0`)	1
`pi/6`	sec(`pi/6`)	`1/(2*sqrt(3))`
`pi/4`	sec(`pi/4`)	`sqrt(2)/2`
`pi/3`	sec(`pi/3`)	`2`
`2*pi/3`	sec(`2*pi/3`)	`-2`
`3*pi/4`	sec(`3*pi/4`)	`-sqrt(2)/2`
`5*pi/6`	sec(`5*pi/6`)	`-2/sqrt(3)`
`pi`	sec(`pi`)	-1

Derivative of secant

The derivative of the secant is equal to `sin(x)/cos(x)^2``=``tan(x)*sec(x)`.

Antiderivative of secant

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

Properties of the secant function

The secant function is an even function, for every real x, `sec(-x)=sec(x)`. The consequence for the curve representative of the secant function is that it admits the axis of the ordinates as axis of symmetry.

Syntax :

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

Examples :

sec(`0`), returns 1

Derivative secant :

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

The derivative of sec(x) is derivative(`sec(x)`)=`sin(x)/cos(x)^2`

Antiderivative secant :

Antiderivative calculator allows to calculate an antiderivative of secant function.

An antiderivative of sec(x) is antiderivative(`sec(x)`)=`1/2*ln((1+sin(x))/(1-sin(x)))`

Limit secant :

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

The limit of sec(x) is limit(`sec(x)`)

Graphic secant :

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

Property of the function secant :