Trigonometric functions in LaTeX
\sin, \cos and \tan (with \cot, \sec, \csc) are LaTeX's built-in operator commands for the trigonometric functions; they set the function name upright with the correct spacing before its argument, instead of italicising it like a variable.
LaTeX command
\sin, \cos, \tanNot the symbol you meant? Draw it to find the command →
Typing sin x by hand without the command italicises every letter, s, i, n, as if they were three multiplied variables, which is both wrong and cramped. \sin x tells LaTeX this is a named function: it prints upright roman letters and adds the small gap a function name needs before its argument.
Powers go directly on the command name, before the argument: \sin^2\theta, not \sin\theta^2. This convention, seen in \sin^2\theta + \cos^2\theta = 1, is the standard way trig identities appear in print, and (\sin\theta)^2 works too when the argument itself is complicated.
Inverse functions have their own commands, \arcsin, \arccos, \arctan, which avoid the ambiguous \sin^{-1} notation some readers misread as a reciprocal. The hyperbolic versions \sinh, \cosh, \tanh, \coth follow the same upright convention.
Other forms
\arcsin, \arccos, \arctaninverse\sinh, \cosh, \tanhhyperbolicExamples
$\sin^2\theta + \cos^2\theta = 1$the Pythagorean identity
$\tan\theta = \dfrac{\sin\theta}{\cos\theta}$tangent as a ratio
$\arcsin(1) = \dfrac{\pi}{2}$the inverse sine
$\sinh x = \dfrac{e^x - e^{-x}}{2}$hyperbolic sine defined via exponentials
$\cos(a-b) = \cos a\cos b + \sin a\sin b$the angle-subtraction formula
Tips and common mistakes
- Never write sin, cos or tan as plain text in maths mode; italic sin reads as s times i times n. Always use the command.
- Write the power on the command name,
\sin^2x, not on the argument,\sinx^2 means something different. \tan,\cot,\secand\cscare all built in alongside\sinand\cos, and\cothis the standard hyperbolic form too, though\sechand\cschare not standard, define them with\operatorname{sech}if you need them.- Use
\arcsin,\arccos,\arctanfor inverses rather than\sin^{-1}, which some readers confuse with 1/\sin. - For sine squared,
\sin^2\thetais the standard form; (\sin\theta)^2 is equivalent and can be clearer when the argument is itself a longer expression.
Working from handwritten notes?
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Convert your maths to LaTeX →FAQ
Why does sin look italic and cramped when I don't use \sin?
Without the command, LaTeX treats each letter as a separate italic variable multiplied together; \sin switches to the built-in operator, which is upright and correctly spaced from its argument.
How do I write inverse sine?
Use \arcsin, for example \arcsin(x); \sin^{-1}(x) is sometimes used instead but can be misread as a reciprocal.
How do I write sine squared?
\sin^2\theta, with the exponent placed on the command itself rather than after the argument.
Is there a LaTeX command for cot, sec and csc?
Yes, \cot, \sec and \csc are all built in alongside \sin, \cos and \tan, and behave the same way.