Property	Value
Hex Value	`$C6`
Categories	Catalog > T Keypad
Localizations	FR: `tan(`

`tan(`

Overview

Returns the tangent of a real number, expression, or list.

Availability: Token available everywhere.

Syntax

tan(value)

Arguments

Name	Type	Optional
value	real\|expression\|real[]

Location

tan

Description

tan(θ) calculates the tangent of the angle θ, which is defined by $\tan \theta=\frac{\sin \theta}{\cos \theta}$

The value returned depends on whether the calculator is in Radian or Degree mode. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion from radians to degrees is angle180/π and from degrees to radians is angleπ/180. The tan( command also works on a list of real numbers.

Since tangent is defined as the quotient of sine divided by cosine, it is undefined for any angle such that cos(θ)=0.

In radians:

tan(π/4)
    1

In degrees:

tan(45)
    1

Advanced Uses

You can bypass the mode setting by using the ° (degree) and ^ʳ (radian) symbols. These next two commands will return the same values no matter if your calculator is in degrees or radians:

tan(45°)
    1

tan(π/4¹ )
    1

Error Conditions

ERR:DATA TYPE is thrown if you supply a matrix or a complex argument.
ERR:DOMAIN is thrown if you supply an angle of π/2±nπ (in radians, where n is an integer) or 90±180n (in degrees, where n is an integer), or when the input is ≥1E12.

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Mr Dino, simplethinker, Timothy Foster, Weregoose, Xeda Elnara.

History

Calculator	OS Version	Description
TI-82	1.0	`tan` added
TI-83	0.01013	Renamed `tan` to `tan(`

Authors: Adrien Bertrand

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