the result is <strong>explicitly undefined</strong>.

If an implementation is capable of exactly representing these inputs,

it <em>should</em> return

+∞ for the asymptotes at <code>90deg + N*360deg</code>,

and −∞ for the asymptotes at <code>-90deg + N*360deg</code>,

but implementations are not required to be able to exactly represent these inputs

(and if they can't, will return whatever the correct numeric answer is

for the closest approximation to the input

they are capable of representing).

Authors <em>must not</em> rely on ''tan()'' returning any particular value

for these inputs.

<details class=note>

<summary>Why are these undefined?</summary>

The tangent function is <em>discontinuous</em> at its asymptotes:

it approaches infinity from one side

<em>and</em> negative infinity from the other side,

and isn't defined at the exact values of the asymptote.

Further, whether or not the asymptotic values

are exactly representable in implementations

depends on how they internally store and manipulate angles;

when written in degrees the values are simple (''90deg'', etc),

but in radians the values are transcendental (''pi / 2'', etc)

and cannot be exactly represented.

So, even defining a specific behavior for these values is difficult;

if an implementation uses radians internally,

it would have to do some fuzzy matching

to return the defined value

when the input is <em>sufficiently close</em> to the asymptote.

The other major language for the Web, JavaScript,

exposes these functions as taking radians only,

so it can't hit the exact asymptotes either

(and this true for most other computer languages, too).

Authors writing code in JS, then,

can't rely on any specific behavior for these values either,

and it's unlikely that their needs in CSS are significantly different.

The suggested behavior for implementations that can exactly represent the asymptote values

preserves round-tripping with the ''atan()'' function:

''tan(atan(X))'' and ''atan(tan(X))''

will both return (approximately) X

for all possible X values,

given this definition.

It also means that within the supported output range of ''atan()'',

the function is continuous.

</details>