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

Tangent function

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

The trigonometric function tangent noted tan, allows to calculate the tangent of an angle online , it is possible to use different angular units :

• radians wich is the angular unit by default,
• degrees or
• gradians.

Calculation of the tangent

Tangent calculating an angle in radians

The tangent calculator allows through the tan function to calculate online the tangent 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 tangent online of `pi/6`, enter tan(`pi/6`), after calculation, the result `sqrt(3)/3` is returned.

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

Calculate the tangent of an angle in degrees

To calculate the tangent 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 tangent of 60, enter tan(60), after calculation, the restults `sqrt(3)` is returned.

Calculate the tangent of an angle in gradians

To calculate the tangent 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 tangent of 50, enter tan(50), after computation, the result `1` is returned.

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

Special tangent values

The tangent admits some special values which the calculator is able to determine in exact forms. Here is the list of the special tangent values:

tan(`2*pi`)	`0`
tan(`pi`)	`0`
tan(`pi/4`)	`1`
tan(`pi/3`)	`sqrt(3)`
tan(`pi/6`)	`sqrt(3)/3`
tan(`2*pi/3`)	`-sqrt(3)`
tan(`3*pi/4`)	`-1`
tan(`5*pi/6`)	`-sqrt(3)/3`
tan(`-2*pi`)	`0`
tan(`-pi`)	`0`
tan(`-pi/4`)	`-1`
tan(`-pi/3`)	`-sqrt(3)`
tan(`-pi/6`)	`sqrt(3)/3`
tan(`-2*pi/3`)	`sqrt(3)`
tan(`-3*pi/4`)	`1`
tan(`-5*pi/6`)	`sqrt(3)/3`

Main properties

`AA x in RR, k in ZZ`,

• `tan(-x)= -tan(x)`
• `tan(x+k*pi)=tan(x)`
• `tan(pi-x)=-tan(x)`
• `tan(pi+x)=tan(x)`
• `tan(pi/2-x)=1/tan(x)`
• `tan(pi/2+x)=-1/tan(x)`

Derivative of tangent

The derivative of the tangent is equal to `1/cos(x)^2`.

Antiderivative of tangent

The antiderivative of the tangent is equal to `-ln(cos(x))`.

Properties of the tangent function

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

Syntax :

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

Examples :

tan(0), returns 0

Derivative tangent :

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

The derivative of tan(x) is derivative(`tan(x)`)=`1/cos(x)^2`

Antiderivative tangent :

Antiderivative calculator allows to calculate an antiderivative of tangent function.

An antiderivative of tan(x) is antiderivative(`tan(x)`)=`-ln(cos(x))`

Limit tangent :

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

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

Inverse function tangent :

The inverse function of tangent is the arctangent function noted arctan.

Graphic tangent :

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

Property of the function tangent :

• 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.