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What is the difference between the geometric secant(the line that cuts two points of a curve) of a curve, and the trigonometric secant(=1/cosinex) ? If they are the same, can you explain how they are the same?

Could you please explain, I am not able to see it intuitively.

Thank you!

zibzabpuzzless
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  • Related (dupe?): https://math.stackexchange.com/questions/1909833/ – DonielF Oct 10 '17 at 18:42
  • In no way is this a duplicate. Similar, in that it relates to a different combination of a trig function and and a trig definitions with the same name, but little to no relation. – Malcolm Anderson Aug 06 '22 at 17:16

2 Answers2

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"Secant" means it cuts the curve. It doesn't have to cut in exactly two points. It could cut the curve three times, or just once.

That said, the trigonometric functions such as tangent and secant describe finite lengths, whereas the geometric tangent and secant are lines of infinite length. There is barely any connection between the two uses of the terms.

If you are likely to get the trigonometric secant mixed up with the tangent, you can recall that when we draw them on a unit circle the tangent is tangent to the circle and the secant cuts across the circle. But I wouldn't look for any connection more meaningful than that.

David K
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Let me Google that for you: https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions (see the diagrams to the right)

Greg Martin
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    Which diagrams are you referring to? – DonielF Oct 10 '17 at 18:40
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    This answer was less than useless. This is like pointing to a library building and saying "your answer is in there." Except that you're pointing to a single chapter in a single book, and saying "the answer is in this chapter."
    Unfortunately, the person was asking about pineapples and you sent them to a chapter about apples. That link only talks about the secant function, and it defines that secant steps from latin secans meaning cutting. There is no mention of the "secant line" in the article. You answer wastes the reader's time without providing value. (I rant rather than down vote)     – Malcolm Anderson Aug 06 '22 at 17:30
  • Feel free to downvote, this is not a great answer.... That being said, the link to a particular spot on the page had changed since I posted this; I fixed it to at least point at the right place. – Greg Martin Aug 06 '22 at 17:34
  • I'd just love to get an answer. I'm studying math and came across "the secant line" which is the average slope between 2 lines. And it's driving me crazy that no one seems to be able so say "why" these two things are called the nearly the same thing ("secant line" vs "secant function"). It could be that they are very related, or completely unrelated. Currently I'm going with, "they're probably related some way, but are functionally 2 very different things." PS - a second pass on that wiki page didn't turn up a reference to anything called "a secant line" - did I miss it? – Malcolm Anderson Oct 03 '22 at 06:49