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Thread: Why is the function called "secant"

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    Junior Member B9766's Avatar
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    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.
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    Re: Why is the function called "secant"

    Quote Originally Posted by B9766 View Post
    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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