Given a right triangle, select a vertex where the hypotenuse and one of the legs meet.
The angle #theta# created by this two sides will be used as a reference point
The side that formed the angle #theta# together with the hypotenuse will be referred to as #adjacent# (side adjacent to the angle). The other side will be referred to as #opposite# (side opposite the angle)
The ratio between the #opposite# and the #"hypotenuse"# is called #"sine" (sin#). The inverse of this ratio is called #"cosecant" (csc#)
#sin theta = "opposite" / "hypotenuse" #
#csc theta = "hypotenuse" / "opposite" = 1 / sin theta#
The ratio between the #adjacent# and the #"hypotenuse"# is called "cosine". The inverse of this ratio is called "secant"
#cos theta = "adjacent" / "hypotenuse" #
#sec theta = "hypotenuse" / "adjacent" = 1 / cos theta#
The ratio between the #opposite# and the #adjacent# is called
#"tangent"#. The inverse of this ratio is called #"cotangent"#
#tan theta = "opposite" / "adjacent"#
#cot theta = "adjacent" / "opposite" = 1 / tan theta#
For example, in a 30-60-90 triangle
#sin 30 = 1 / 2#
#cos 30 = 3^(1/2)/2#
#tan 30 = 1 / 3^(1/2)#
#csc 30 = 2#
#sec 30 = 2/3^(1/2)#
#cot 30 = 3^(1/2)#
#sin 60 = 3^(1/2)/2#
#cos 60 = 1 /2 #
#tan 60 = 3^(1/2)#
#csc 60 = 2/3^(1/2)#
#sec 60 = 2#
#cot 60 = 1 / 3^(1/2)#
