# the units corresponding some mathematical functions

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I had previously thought that this topic would suit in physics but decided in maths, however if not, I apologise in advance.

Question:

can we describe the unit of x in sine function in centimeter?

for instance sin(x) is equal to 1 cm, where x is equal to π/2 centimeter.

This question was a part of one of projects.

Unfortunately I am not good in physics  in the current position although I am willing to learn it but I saw (almost) no problem regarding its mathematical side.

(because in fact as we know that sine function's domain set was R and value set was [-1,1] Maybe I am again failing because here the values in domain sets are angles)

Edited by ahmet
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The x in sin(x) has no physical units.  It is usually in terms of radians or degrees.  sin(x) also has no physical dimension - usual definition is the ratio of two lengths.

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Just now, mathematic said:

The x in sin(x) has no physical units.  It is usually in terms of radians or degrees.  sin(x) also has no physical dimension - usual definition is the ratio of two lengths.

and, so...?

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So the equation has to be Asin(ax) where a has units of 1/cm and A has units of cm

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Just elaborating on what @mathematic and @swansont have said...

It wouldn't even make much sense geometrically. An angle is naturally (more simply) expressed as a ratio of lengths (arc/radius). The sine itself is a ratio of lengths too.

If you define x in cm it's as much as saying that there's one circle which is the mother of all circles. The 1-cm radius circle!!

A 1-cm-radius circle is a French thing. Why should a circle be French?

(There is a 1-m bar in Paris keeping this standard of length.)

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13 hours ago, swansont said:

So the equation has to be Asin(ax) where a has units of 1/cm and A has units of cm

Hi,

I might have misunderstood somewehere.not sure.

This function Asin(ax) is periodical function and the period here is $\frac {2\pi}{|a|}$ the values of peak can be set by A.

Exactly the thing I am asking is that whether ax could be defined with centimeter units.

12 hours ago, joigus said:

A 1-cm-radius circle is a French thing. Why should a circle be French?

(There is a 1-m bar in Paris keeping this standard of length.)

pahah   why not: not for french but I am sure that the circle on Gold Lira (Turkish Republic Gold ) is turkish.

Edited by ahmet
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1 hour ago, ahmet said:

Hi,

I might have misunderstood somewehere.not sure.

This function Asin(ax) is periodical function and the period here is 2π|a| the values of peak can be set by A.

Exactly the thing I am asking is that whether ax could be defined with centimeter units.

No. It must be unitless as mathematic told you. If x is in cm, a must have units of 1/cm

A sets the amplitude and also the units of the result, since sine returns a unitless value

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54 minutes ago, swansont said:

No. It must be unitless as mathematic told you. If x is in cm, a must have units of 1/cm

A sets the amplitude and also the units of the result, since sine returns a unitless value

Thus...this means that,we cannot calculate x axis' length that sine function passes over it (at 0,π , 2π , 3π..etc)

in that, could you assume please we turn sin(x) 360 degree around sin(x) + t (t here is any natural number)

how will/must the length of the object be measured?

Edited by ahmet
grammatical failure
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42 minutes ago, ahmet said:

Thus...this means that,we cannot calculate x axis' length that sine function passes over it (at 0,π , 2π , 3π..etc)

The sine function doesn’t give you that, so that’s not the way to calculate it

42 minutes ago, ahmet said:

in that, could you assume please we turn sin(x) 360 degree around sin(x) + t (t here is any natural number)

how will/must the length of the object be measured?

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2 hours ago, swansont said:

The sine function doesn’t give you that, so that’s not the way to calculate it

I think I do not mention about that.

and

you seem like you are not aware from calculating integrals (e.g.:  calculation of volumes, and mmm specific integrals (e.g. surface integrals and or green ,stokes , diverjans theorems)

sorry,I do not allege anything ,but your comment cause me to suppose something in this way.

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5 minutes ago, ahmet said:

you seem like you are not aware from calculating integrals (e.g.:  calculation of volumes, and mmm specific integrals (e.g. surface integrals and or green ,stokes , diverjans theorems)

I am aware, but none of that was brought up in this thread. You have to provide context. We can’t read your mind.

So I ask again: to what object do you refer?

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consider these: how were we calculating these object's volume?

--->> an abject has vivianni window at its one side and other sides are regular.

--->> an object that created by turning $y=x^{3}$ function arpound x=y function (360 degree)

I underline the obtained object's lengths. these objects have to have length.

Edited by ahmet
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The units come into these calculations through the differentials. If you integrate dx, for example, you can have units on the limits of the integration, if it’s appropriate for the problem.

But it’s not proper if it involves a trig function.

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2 minutes ago, swansont said:

So I ask again: to what object do you refer?

The object I refer is that any object created by any function (by turning it around another function that offset of that function. (but here that function is :sine function))

(to better understand,I recommend this : first turn that function around the offset function and fill the inside of tunnel with glass.object is clear??

wait please ,I shall draw something by my hand..

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1 minute ago, ahmet said:

The object I refer is that any object created by any function (by turning it around another function that offset of that function. (but here that function is :sine function))

(to better understand,I recommend this : first turn that function around the offset function and fill the inside of tunnel with glass.object is clear??

Then the units would be in the amplitude, A

Not in the sin function, or its argument

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mm ,if I understand  correctly you express this one: "the function itself does not come with any unit or not being calculated with any unit, but you also express that anyone can give any unit to it."

if you would like,I can upload the picture,but now I think it does not seem like a requirement,it seems the question is being resolved.

I mean something like these: after drawing the graph of function of sine. (for instance with R) this will bring you a classic graph of sine function.

but for instance you probably said that I could mark π/2 cm , πcm , 3π/2cm, 2πcm, etc..at each points. (But R does not write so,I mean if I would,I can add cm or mm or any else unit) Right?

for instance with what type of unit the π length should/will be defined?

(if I understood correctly,you say that I was free..to select any unit (?))

π is only a quantity ,we normally need something to define (for instance here) the length

but with which unit?

Edited by ahmet
spelling errors
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The units would depend on the problem, and you have not provided enough information to answer. Other than it would be a unit of length.

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ok , if you mean I would be free to select any unit depending to the type of problem,then I think..my question has been definitely resolved.

yes, if so,I would just say: MANY MANY THANKS

Edited by ahmet
A CREATURE SHOWING HIS BEAUTIFUL HEAD. HAHA :)
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You appear to be confusing "mathemtatics" with "applictions of mathematics".  In mathematics, we have abstract functions, such as "y= bsin(ax)", "y= be^(ax)", etc. There are NO "units" associated with x or y.  IF we want to apply those to specific problems, then you need to choose units for x and y that correspond to those applications.  For example, if you have a problem in which you need need to calulate  an ocean wave you might well choose a sine or cosine function, the "ideal" periodic functions, then "x" might be measured in "meters".  In order to be able  to use bsin(ax) or be^(ax) we must have "a" having units of "1/meter" as swansont and others said.  And if the function is to return "meters" then "b" must have units of "meters".   (Of course, it might occure that a and/or b have numerical value of "1" so they are obscured but units are still there.)

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• 3 weeks later...
On 10/14/2020 at 1:43 AM, HallsofIvy said:

You appear to be confusing "mathemtatics" with "applictions of mathematics".  In mathematics, we have abstract functions, such as "y= bsin(ax)", "y= be^(ax)", etc. There are NO "units" associated with x or y.  IF we want to apply those to specific problems, then you need to choose units for x and y that correspond to those applications.  For example, if you have a problem in which you need need to calulate  an ocean wave you might well choose a sine or cosine function, the "ideal" periodic functions, then "x" might be measured in "meters".  In order to be able  to use bsin(ax) or be^(ax) we must have "a" having units of "1/meter" as swansont and others said.  And if the function is to return "meters" then "b" must have units of "meters".   (Of course, it might occure that a and/or b have numerical value of "1" so they are obscured but units are still there.)

to be honest,I am feeling myself both badly and well. because ..while I understand that the units just depend on us (for instance I could draw y=sin(x) functions graph both in cm and mm , I think I have badly told the case or could not ensure the listener / reader understand  well in the project..

so, freedom is already always good , but I have not expressed the case well in my project,this is not good,it is bad.

thanks to everyone for participation to this thread.

Edited by ahmet
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58 minutes ago, ahmet said:

to be honest,I am feeling myself both badly and well. because ..while I understand that the units just depend on us (for instance I could draw y=sin(x) functions graph both in cm and mm , I think I have badly told the case or could not ensure the listener / reader understand  well in the project..

so, freedom is already always good , but I have not expressed the case well in my project,this is not good,it is bad.

thanks to everyone for participation to this thread.

I'm glad to see you came through today's R scale 7 earthquake, hopefully you were not too badly affected.

Since your internet is still working here are a bunch of 4 lectures in pdf that should help you with English Maths terminology.

Note the chapter numbers at the end.
Change these from 1 through 4 to get all 4.

Chapter 4 (Rotations) is particularly relevent to this thread.
In particular you should note the difference between finite rotations and continuous rotations in dimension theory, vector theory and calculus.

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1 hour ago, studiot said:

I'm glad to see you came through today's R scale 7 earthquake, hopefully you were not too badly affected

thank you really I heard / learnt it from the news.

Meanwhile, Do you know, I was teaching in istanbul but passed to antalya just because of the potentiality of earthquake , ahaha I escaped

mmm although written documents seems better (I mean I enjoy them) ,I shall again try to deal/watch the video.

thanks.

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2 hours ago, ahmet said:

thank you really I heard / learnt it from the news.

Meanwhile, Do you know, I was teaching in istanbul but passed to antalya just because of the potentiality of earthquake , ahaha I escaped

mmm although written documents seems better (I mean I enjoy them) ,I shall again try to deal/watch the video.

thanks.

pdf files are documents for reading , they are not videos for watching.

ph.ed.ac.uk is the postgraduate Physics department of the University of Edinburgh.

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13 hours ago, studiot said:

pdf files are documents for reading , they are not videos for watching.

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