# TI-BASIC:Tan

**Command Summary**

Returns the tangent of a real number.

**Command Syntax**

tan(*angle*)

**Menu Location**

Press TAN

TI-83/84/+/SE

1 byte

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

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 angle*180/π and from degrees to radians is angle*π/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/4^^r) 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)