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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.