# What is a tangent? (multiple meanings)

• graphking
In summary, the word "tangent" has two main meanings: in mathematics, it refers to both a trigonometric function and the intersection of two geometric objects, and it is important to consider the context in order to avoid misunderstandings in academic writing. These two meanings are related, as the length of the tangential line on the unit circle corresponds to the value of the tangent function. However, they have distinct uses in different contexts and should not be confused with each other. In the field of STEM, there are many homonyms and it is crucial to use precise mathematical language to avoid confusion.

#### 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.

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##.

DaveE and TeethWhitener
Thanks! But I still think the two meanings are really of great difference, though:
anuttarasammyak said:
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.

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.

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.