Trig Functions: The Functions

sine(q) = opp/hyp | cosecant(q) = hyp/opp |

cosine(q) = adj/hyp | secant(q) = hyp/adj |

tangent(q) = opp/adj | cotangent(q) = adj/opp |

The functions are usually abbreviated:
sine (sin), cosine (cos), tangent (tan)
cosecant (csc), secant (sec), and cotangent (cot).

It is often simpler to memorize the the trig functions in terms
of only sine and cosine:

sin(q) = opp/hyp | csc(q) = 1/sin(q) |

cos(q) = adj/hyp | sec(q) = 1/cos(q) |

tan(q) = sin(q)/cos(q) | cot(q) = 1/tan(q) |

inverse functions
arcsine(opp/hyp) = q |
arccosecant(hyp/opp) = q |

arccosine(adj/hyp) = q |
arcsecant(hyp/adj) = q |

arctangent(opp/adj) = q |
arccotangent(adj/opp) = q |

The functions are usually abbreviated:
arcsine (arcsin), arccosine (arccos), arctangent (arctan)
arccosecant (arccsc), arcsecant (arcsec), and arccotangent (arccot).
According to the standard notation for inverse functions (f^{-1}),
you will also often see these written as
sin^{-1}, cos^{-1}, tan^{-1}
arccsc^{-1}, arcsec^{-1}, and arccot^{-1}.
*Beware*, though, there is another common notation that
writes the square of the trig functions, such as (sin(x))^{2}
as sin^{2}(x). This can be confusing, for you then
*might* then be lead to think that sin^{-1}(x) =
(sin(x))^{-1}, which is *not* true.
The negative one superscript here is a special notation that denotes
inverse functions (not multiplicative inverses).

See also: overview.