How to use the Excel TAN function

Summary

The Excel TAN function returns the tangent of angle given in radians. To supply an angle to TAN in degrees, multiply the angle by PI()/180 or use the RADIANS function to convert to radians.

Purpose

Get the tangent of an angle

Return value

The tangent value.

Syntax

=TAN (number)

Arguments

number - The angle in radians for which you want the tangent.

Version

Excel 2003

Usage notes

The TAN function returns the tangent of an angle provided in radians. In geometric terms, the tangent of an angle returns the ratio of a right-triangle's opposite side over its adjacent side. For example, the the tangent of PI()/4 (45°) returns the ratio of 1.0.

=TAN(PI()/4) // Returns 1.0

Using Degrees

To supply an angle to TAN in degrees, multiply the angle by PI()/180 or use the RADIANS function to convert to radians. For example, to get the TAN of 60 degrees, you can use either formula below:

=TAN(60*PI()/180)
=TAN(RADIANS(60))

Explanation

Graph of Tangent Function

The graph of the tangent function, shown above, visualizes the output of the function for angles from 0 to a full rotation corresponding to the range [0, 2π]. The function has two vertical asymptotes within the range [0, 2π] where the output diverges to infinity. The tangent function can be equivalently defined in terms of SIN and COS:

=TAN(θ) = SIN(θ)/COS(θ)

Related functions

Excel SIN Function

The Excel SIN function returns the sine of angle given in radians. To supply an angle to SIN in degrees, multiply the angle by PI()/180 or use the RADIANS function to convert to radians.

Excel COS Function

The Excel COS function returns the cosine of an angle given in radians. To supply an angle to COS in degrees, use the RADIANS function to convert to radians.