Cosine Oxford Dictionary Definition

[shahar]

The Oxford Dictionary is defining Cosine by two definition:
1 [That's clear to me] (of a triangle) the ratio of the length of the adjacent side to the hypotenuse.
2 [This is not clear to me:] (in a circle with a pair of axes meeting at the centre) a line from a point where a sine meets an arc perpendicular to a radius that is at right angles to the on at the other end of the sine."
O.K. What is meaning of the underlined text?
[I think I understand it if it will be written in another words]

 

[The Highlander]

The Oxford Dictionary is defining Cosine by two definition:
1 [That's clear to me] (of a triangle) the ratio of the length of the adjacent side to the hypotenuse.
2 [This is not clear to me:] (in a circle with a pair of axes meeting at the centre) a line from a point where a sine meets an arc perpendicular to a radius that is at right angles to the on at the other end of the sine."
O.K. What is meaning of the underlined text?
[I think I understand it if it will be written in another words]

I can't check the definitions you provide (because access to the OED is not free, at least in the UK it isn't), however, what you have written appears to be missing at least one word: "to the ???? on at the other end" (there appears to be something missing where I have inserted the question marks).

I am also concerned (as I know English is not your first language) that what you have posted may be a (Google?) translation of something you have seen in another language (Hebrew?).

How/where did you find these 'definitions'?
Do you have paid access to the OED?
Have your definitions been translated into English?
Please check that what you have posted is complete.

 

[Dr.Peterson]

I think a picture will be clearer:

​

I've put a circle at the origin of a coordinate system, and drew a line from point C (the end of an arc) perpendicular to the axis throught the other end of the arc. Segment AD is the cosine; CD is the sine.

I don't think their definition is at all clear! Presumably their definition of sine would help.

But you have clearly typed something wrong, since there are grammatical errors in your quote! (E.g. I think it's "to the one at the other end".) Which Oxford dictionary is this? I can't find this definition online.

It isn't this, for example:

cosine noun - Definition, pictures, pronunciation and usage notes | Oxford Advanced Learner's Dictionary at OxfordLearnersDictionaries.com

Definition of cosine noun in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.

www.oxfordlearnersdictionaries.com

 

[shahar]

2 [This is not clear to me:] (in a circle with a pair of axes meeting at the centre) a line from a point where a sine meets an arc perpendicular to a radius that is at right angles to the one at the other end of the sine.

 

[The Highlander]

I think a picture will be clearer:

View attachment 39064​

I've put a circle at the origin of a coordinate system, and drew a line from point C (the end of an arc) perpendicular to the axis throught the other end of the arc. Segment AD is the cosine; CD is the sine.

I don't think their definition is at all clear! Presumably their definition of sine would help.

But you have clearly typed something wrong, since there are grammatical errors in your quote! (E.g. I think it's "to the one at the other end".) Which Oxford dictionary is this? I can't find this definition online.

Agreed. except, shouldn't that be a unit circle for the segments AD to be the Cosine and CD the Sine?

 

[shahar]

I think a picture will be clearer:

View attachment 39064​

I've put a circle at the origin of a coordinate system, and drew a line from point C (the end of an arc) perpendicular to the axis throught the other end of the arc. Segment AD is the cosine; CD is the sine.

I don't think their definition is at all clear! Presumably their definition of sine would help.

But you have clearly typed something wrong, since there are grammatical errors in your quote! (E.g. I think it's "to the one at the other end".) Which Oxford dictionary is this? I can't find this definition online.

It a paper book definition.
Thanks.
I know that writing very little part of the dictionary is allowed because we doesn't do commercial or profit with my post. This is the meaning of copyright laws in Israel and I believe it is as same as in US or UK

 

[Dr.Peterson]

I should add that I am not really familiar with this definition of cosine as a line segment, though I can imagine it, possibly as an old definition no longer used.

It a paper book definition.

Can you give us an image of this definition? And tell us the full name of your dictionary; I very much doubt that you own the full Oxford English Dictionary, but they make others, like the one I referred to online.

 

[shahar]

here:

 

[shahar]

I should add that I am not really familiar with this definition of cosine as a line segment, though I can imagine it, possibly as an old definition no longer used.



Can you give us an image of this definition? And tell us the full name of your dictionary; I very much doubt that you own the full Oxford English Dictionary, but they make others, like the one I referred to online.

Do you want the definition itself?

 

[Dr.Peterson]

Now show us the image I asked for, of the definition.

Is it true that what you quoted is a translation from Hebrew? I'll want to see it even if it is in Hebrew.

 

[The Highlander]

I should add that I am not really familiar with this definition of cosine as a line segment, though I can imagine it, possibly as an old definition no longer used.

Any time I've seen the Sine & Cosine ratios defined that way, it has always been using a Unit circle. ie: with a radius of 1, centred at the Origin.

That way the x & y coordinates of any point on the circumference immediately provide the Cosine & Sine ratios ratios respectively (because the hypotenuse of the resulting right-angled triangle is 1 and the line segments (from the origin to x & y) are, therefore, divided by 1 to get the corresponding Trig. ratios.

This definition has the advantage of 'automatically' giving the correct signs to the ratios.

In your example (diagram) the line segments AD & CD would not give the correct values for the ratios themselves as they would first need to be divided by 3 (the radius of your circle).

 

[Dr.Peterson]

I found an old edition of the book at archive.org:

Oxford student's dictionary for Hebrew speakers : Free Download, Borrow, and Streaming : Internet Archive

[8], 904 pages ; 23 cm

archive.org

Oxford student's dictionary for Hebrew speakers : Free Download, Borrow, and Streaming : Internet Archive

[8], 904 pages ; 23 cm

archive.org

I'd say this is just a very faulty definition, unless perhaps, as I suggested, it is an old historical usage. Even so, the wording is poor.

It should not be in a student's dictionary!

And you should not use this dictionary to understand mathematical terms.

 

[The Highlander]

I found an old edition of the book at archive.org:

Oxford student's dictionary for Hebrew speakers : Free Download, Borrow, and Streaming : Internet Archive

[8], 904 pages ; 23 cm

archive.org

View attachment 39066

Oxford student's dictionary for Hebrew speakers : Free Download, Borrow, and Streaming : Internet Archive

[8], 904 pages ; 23 cm

archive.org

View attachment 39068

I'd say this is just a very faulty definition, unless perhaps, as I suggested, it is an old historical usage. Even so, the wording is poor.

It should not be in a student's dictionary!

And you should not use this dictionary to understand mathematical terms.

And, again, these definitions (which are unnecessarily obtuse) only work if the "circle" mentioned is a unit circle.

 

[Dr.Peterson]

And, again, these definitions (which are unnecessarily obtuse) only work if the "circle" mentioned is a unit circle.

Yes, of course. You've said it enough times that I don't need to say it too. (Your comment is included in my "very faulty".) I've been focusing on another track, though it is admittedly unlikely.

If I had access to the OED I would look to see if my wild speculation that "cosine" might have once been used to mean "the adjacent side" has any truth to it; but it does seem far more likely that they simply omitted to say "unit circle". Either way, it's a horrible definition, and I am very curious as to how it could ever have found its way into any Oxford dictionary of current English.

The Oxford Students Dictionary

Oxford Students Dictionary : Oxford Dictionary : Free Download, Borrow, and Streaming : Internet Archive

archive.org

says what we expect it to say:



But that lacks the unit-circle definition (or equivalent), so it doesn't cover all angles -- making this dictionary also somewhat defective for learning math terms!

Looking further, I find a 1988 edition of the Students Dictionary,

Oxford student's dictionary of current English : Hornby, Albert Sydney : Free Download, Borrow, and Streaming : Internet Archive

768p. in various pagings ; 20cm

archive.org

that has our faulty definitions, so they were not invented for the Hebrew edition!



I'll probably keep looking for another source of this meaning, in order to determine whether they really meant what they say, or intended to say either ratio or unit circle.

 

[Dr.Peterson]

When I went to work today, I took the time to look in the school library, to see what the OED says. I found this:



So my guess was right; at one time "sine" did refer to the segment, regardless of the radius, though the modern usage refers to the ratio.

Nearby on the shelf was the Random House Webster's Unabridged Dictionary, which had a similar mention:



(The entries for cosine aren't helpful.)

But I found no clear indication of how long ago this geometrical definition might have been used, or why the 1988 Student's Dictionary would have given it, since as far as I can tell, it is very old.