what is the definition of SECANTS?

The algebraic definition of a secant is the length of line defined by two points as follows:

Secant = (f(b) - f(a)) / (b - a)

The secant is the reciprocal of the cosine.

When a & b are very close to each other (i.e., b - a = some very tiny value near 0), then the secant is nearly equal to the tangent.

secant is the inverse of cosine.

so where cosine is the length of the adjacent side to the angle over the length of the hypotenuse, secant is the hypotenuse over the adjacent side.

cosecant, then, is the opposite of sine.

sine is length of side opposite over hypotenuse; cosecant is hypotenuse over opposite side.

sadly, this only works for right triangles, but it's a start. i know you can use it on other triangles, but i don't know how to do it anymore.