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)
