Inverse trigonometric functions

Inverse trigonometric functions are special functions that 'undo' the basic trigonometric functions (sine, cosine, tangent). For example, if $y = an x$, then $x = an^{-1} y$ (also written as $x = ext{arctan} hinspace y$). Because trigonometric functions are not one-to-one over all real numbers, we restrict their domains to make their inverses well-defined.

Important properties

• The inverse sine function, $y = ext{arcsin} hinspace x$, gives the angle whose sine is $x$, with $-1 \\leq x \\leq 1$ and -rac{}{2} \\leq y \\leq rac{}{2}.

• The inverse cosine function, $y = ext{arccos} hinspace x$, gives the angle whose cosine is $x$, with $-1 \\leq x \\leq 1$ and 0 \\leq y \\leq .

• The inverse tangent function, $y = ext{arctan} hinspace x$, gives the angle whose tangent is $x$, with $x \\in \\mathbb{R}$ and -rac{}{2} \\lt y \\lt rac{}{2}.

• Each inverse trigonometric function has a specific range (called its principal value branch) so that it is a function.