Math functions (LaTeX2e unofficial reference manual (November 2018))

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### 16.3 Math functions

These commands produce roman function names in math mode with proper spacing.

`\arccos`

  Inverse cosine

`\arcsin`

  Inverse sine

`\arctan`

  Inverse tangent

`\arg`

  Angle between the real axis and a point in the complex plane

`\bmod`

  Binary modulo operator, used as in `\( 5\bmod 3=2 \)`

`\cos`

  Cosine

`\cosh`

  Hyperbolic cosine

`\cot`

  Cotangent

`\coth`

  Hyperbolic cotangent

`\csc`

  Cosecant

`\deg`

  Degrees

`\det`

  Determinant

`\dim`

  Dimension

`\exp`

  Exponential

`\gcd`

  Greatest common divisor

`\hom`

  Homomorphism

`\inf`

  Infinum

`\ker`

  Kernel

`\lg`

  Base 2 logarithm

`\lim`

  Limit

`\liminf`

  Limit inferior

`\limsup`

  Limit superior

`\ln`

  Natural logarithm

`\log`

  Logarithm

`\max`

  Maximum

`\min`

  Minimum

`\pmod`

  Parenthesized modulus, as used in `\( 5\equiv 2\pmod 3 \)`

`\Pr`

  Probability

`\sec`

  Secant

`\sin`

  Sine

`\sinh`

  Hyperbolic sine

`\sup`

  sup

`\tan`

  Tangent

`\tanh`

  Hyperbolic tangent

The `amsmath` package adds improvements on some of these, and also allows you to define your own. The full documentation is on CTAN, but briefly, you can define an identity operator with `\DeclareMathOperator{\identity}{id}` that is like the ones above but prints as ‘`id`’. The starred form `\DeclareMathOperator*{\op}{op}` sets any limits above and below, as is traditional with `\lim`, `\sup`, or `\max`.

Unofficial LaTeX2e reference manual