# Thread: Why is the function called "secant"

1. ## Why is the function called "secant"

Starting calculus now and just ran through using limits to go from a secant line to a tangent line. A light bulb went on for me when I realized that a tangent line to a circle of radius = 1 is described by the tangent function because:
$tan \theta = \dfrac{opposite}{adjacent} = opposite$ for $adjacent = r = 1$

Part of calculating the tangent begins with a secant line, defined as a line intersecting the curve in two points. It makes since, given that secant means "to cut or sever" in greek.

But why then, is the trigonometric function named "secant"? I don't see a relationship between $sec \theta = \dfrac{hypotenuse}{adjacent}$ and a secant line.

2. ## Re: Why is the function called "secant"

Originally Posted by B9766
Starting calculus now and just ran through using limits to go from a secant line to a tangent line. A light bulb went on for me when I realized that a tangent line to a circle of radius = 1 is described by the tangent function because:
$tan \theta = \dfrac{opposite}{adjacent} = opposite$ for $adjacent = r = 1$
Part of calculating the tangent begins with a secant line, defined as a line intersecting the curve in two points. It makes since, given that secant means "to cut or sever" in greek.
But why then, is the trigonometric function named "secant"? I don't see a relationship between $sec \theta = \dfrac{hypotenuse}{adjacent}$ and a secant line.
I Latin the verb secare means "to cut". A Secant of a of a curve (circle) is a line that cuts the curve in two points.