# Refresh my memory. Geometry

**URL:** <https://boards.straightdope.com/t/refresh-my-memory-geometry/489116>\
**Category:** Factual Questions\
**Created:** [March 11, 2009, 7:52pm UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116 "2009-03-11T19:52:45Z")\
**Posts on this page:** 3\
**Page:** 2

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**Author:** ![Peter\_Morris](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/peter_morris/32/359_2.png) [@Peter\_Morris](https://boards.straightdope.com/u/Peter_Morris)\
**Post date:** [March 12, 2009, 2:18pm UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/21 "2009-03-12T14:18:55Z")

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> [@KCB615](#):
>
> Some Old Horse Caught Another Horse Taking Oats Away.

Silly Old Harry  
Caught A Herring  
Trawling Off America

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**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\
**Post date:** [March 12, 2009, 6:55pm UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/22 "2009-03-12T18:55:27Z")

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> [@DSYoungEsq](#):
>
> Actually, you are a little incorrect about sine, cosine and especially tangent. The function we call “tangent” derives directly from the concept of a tangent to a circle, just as the function we call “secant” derives from a secant. So it is possible, by teaching the concept using the unit circle to give them a way to understand trigonometric functions without having to have them simply memorize a series of apparently arbitrary relationships. Which is how _I_ avoid worrying about SOHCAHTOA (except for those who insist upon some such device, and can’t get by without it). 🙂

Well, there’s still the problem that how many kids know the word “secant” in the other sense to begin with, and so on for “sine” and whatnot. 🙂

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**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\
**Post date:** [March 12, 2009, 8:04pm UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/23 "2009-03-12T20:04:26Z")

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(But I do agree that all the trigonometric functions are better taught via the unit circle than via magnitude ratios in right triangles; cosine and sine as X and Y coordinates, respectively, as one rotates counterclockwise from the right, tangent as the slope of the radius, etc. Much more clear what’s going on with the sign of the result and with negative, obtuse, or “improper” angles, much easier to explain where the differentiation rules come from, and so on. I’m just not sure that it would be particularly helpful to try and clarify “Wait, which one is sine and which one is cosine?” by drawing on non-existent prior memories of the terms being used in some previous fashion, or similarly of what a “secant” is in this context and why its length should happen to be the reciprocal of the cosine, and so on; when these come up, I still can’t see any better resort than to rote memorization: “Cosine is the X coordinate; Sine is the Y coordinate; Secant is 1/cosine…”.)

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