Why is the function called "secant"

Aug 2016
74
3
Plymouth, MA
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.
 

Plato

MHF Helper
Aug 2006
22,475
8,643
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.
 
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