What is a tangent? (multiple meanings)

[graphking]

how many different meanings do you guys know, towards the word "tangent"?
in science, I already know 2 meanings: the functions similar to sin, cos, cot, and it is tan;
it means two geometry objects are intersected, and they touch each other closely.
so I wonder if the different meanings would cause misunderstanding of the academic article.
P.S. I haven't met misunderstandings like this in academics for years.

 

[anuttarasammyak]

Two meanings you show have common sense, say unit circle centered at the Origin has tangential line at (1,0), the part of tangential line between intersection with line of counter clockwise angle $\theta$ measured from x-axis through the Origin and (1,0), has length $\tan \theta$.

 

[TeethWhitener]

Here's a picture to visualize @anuttarasammyak 's excellent answer:
https://en.wikipedia.org/wiki/Trigonometric_functions#/media/File:TrigFunctionDiagram.svg

 

[graphking]

Thanks! But I still think the two meanings are really of great difference, though:

Two meanings you show have common sense, say unit circle centered at the Origin has tangential line at (1,0), the part of tangential line between intersection with line of counter clockwise angle $\theta$ measured from x-axis through the Origin and (1,0), has length $\tan \theta$.

have figured that tan is equal to some part of a tangential line.

 

[anuttarasammyak]

They have different usage. That is why we coin the words tangent, tangential line, and tan. I just mention they may have a same roots in coining.

 

[DaveE]

Like most language, it's all about context. In many decades in STEM, I don't recall confusing a tangent line with the tangent function. I think you'll find lots of homonyms in STEM, which is why we like mathematical descriptions so much.

 

[graphking]

Yes, thank you for your reply!