Names of elements of any equation

[pairofstrings]

Hello.
I came across a Quadratic Equation that looks like this.
5x² + 4x + 9 = 0.

1. The '5' in the above equation is called Quadratic Coefficient.
2. The '4' in the above equation is called Linear Coefficient.
3. The '9' in the above equation is called Constant.
4. The 'x' in the above equation is called Variable.
5. The '2' in the above equation is called Power.

But if I assume a Trigonometric Equation like this.
y = 4 sin(x) + 4 cos^2x(x)

1. What is sine called which has coefficient of '4'?
2. What is 'x' called which is seen in first term and second term of the equation?
3. What is 'y'?
4. What do I Google to find the names of the elements associated with any equation?
5. Are there any more names that are used for the elements of any equation when I talk mathematics?

Thank you.

 

[member 587159]

Sorry to tell you this, but these are things that actually really don't matter. Giving everything a specific name defeats the purpose of mathematics being a language on its own. But if you really want to know:

- x is a variable
- y is a function of x, this means, for each x that I fill in I have a unique y
- no idea what the coefficient with a sine is called. If we have something like y = Asinx then A is called amplitude, but here there is the disturbing $4cos^{2x}(x)$ term as well

 

[pairofstrings]

mathematics being a language on its own

Does it mean that Mathematics is work of humans and for a mysterious reason it works?

My question is:

If I want to talk about any mathematical equation then the only words any equation can be described by is coefficient, variable, constant, power?

How do I describe presence of Sine function or Integral or Derivative in any equation?

I have a belief that a mathematical equation can contain various constructs of Trigonometry, Integrals, Derivatives in the same equation at once - in such case how do I convey the meaning of the equation or describe the equation to the second person?

Is it valid to have constructs from multiple areas of mathematics in one statement - it may describe something, right?

 

[Mark44]

Does it mean that Mathematics is work of humans and for a mysterious reason it works?

My question is:

If I want to talk about any mathematical equation then the only words any equation can be described by is coefficient, variable, constant, power?

Power applies only when some variable or other expression is raised to some power (has an exponent).

How do I describe presence of Sine function or Integral or Derivative in any equation?

The equation pretty much describes itself. There's no need that I can see for a special word to describe this.

I have a belief that a mathematical equation can contain various constructs of Trigonometry, Integrals, Derivatives in the same equation at once - in such case how do I convey the meaning of the equation or describe the equation to the second person?

Tell the other person the equation. That should be sufficient.

Is it valid to have constructs from multiple areas of mathematics in one statement - it may describe something, right?

An equation can involve trig functions, derivatives, integrals, radicals, fractions, whatever.

 

[mfb]

How do I describe presence of Sine function or Integral or Derivative in any equation?

Just say "sine of whatever", "integral of whatever" and so on.

"Prefactor" is a more general name for constants that are in a product with something else, e. g. the 4 in $4 \cos^2(x)$.

 

[pairofstrings]

1.

y = 4 sin(x) + 4 cos^2x(x)

Is it correct to say that "sin(x) is trigonometric function which has a coefficient '4'"?

2.
y = ∫x dy/dx + x sin(x) dy/dx
How do I talk about first term and second term?
For the above equation, can I say that: First term has Integral Derivative of 'x' with respect to 'x', second term has Derivative of Trigonometric function sin(x) with respect to 'x' which is multiplied with variable 'x'?

3.
y = ∫x dy/dx + x sin(x) dy/dx
What umbrella name can dy/dx or sin(x) carry?

I am aware of words: Coefficient, Variable, Constant - these can describe the equation. But if I have an umbrella name for dy/dx and sin(x) then I can add that name to the catalog, which can now become Coefficient, Variable, Constant, Umbrella name?

What could that Umbrella name be?
I think that the Umbrella name can be Concept.

 

[jbriggs444]

Do concepts require names?

 

[mfb]

How do I talk about first term and second term?

Call them "first term" and "second term".
The integral is ill-defined, by the way.

Don't spend time on naming things. This is not mathematics.

 

[Mark44]

Don't spend time on naming things. This is not mathematics.

+1

 

[pairofstrings]

Don't spend time on naming things. This is not mathematics.

Okay. I agree that having lot of names to describe something is stressful but on the other side I think that knowing the vocabulary of Mathematics will make my Mathematics stronger. No?

Do concepts require names?

I think that I can assume that something called 'Permutation and Combination' a Concept because it let's Mathematics speak about something. No?
Am I stretching the word Concept too far?

Firstly, I doubt if the word 'Concept' can be used to convey Sine and dy/dx as Umbrella name because the words Coefficient, Variable, Constant can also be called Concepts or Supporting Concepts(?) when used with Sine or dy/dx.

 

[symbolipoint]

This discussion reminds me of learning Grammar, and the names of the "parts of speech". The instruction that comes in Learning of Mathematics includes the terminology of the parts of what you study. This terminology helps in communicating. It is a moderately stressed thing but should not seem stressful.

 

[Mark44]

Okay. I agree that having lot of names to describe something is stressful but on the other side I think that knowing the vocabulary of Mathematics will make my Mathematics stronger. No?

Overall, probably not. It's helpful in being able to communicate when describing an equation, but the vocabulary is not as important in actually doing the mathematics. This is a point that has already been made.

I think that I can assume that something called 'Permutation and Combination' a Concept because it let's Mathematics speak about something. No?
Am I stretching the word Concept too far?

What's the point of calling, say, Permuation and Combination a concept? "Concept" is such a broad word as to be nearly meaningless here.

Firstly, I doubt if the word 'Concept' can be used to convey Sine and dy/dx as Umbrella name because the words Coefficient, Variable, Constant can also be called Concepts or Supporting Concepts(?) when used with Sine or dy/dx.

If you want umbrella terms, the sine function is one of several trigonometry functions. The terms coefficient, variable, and constant are terminology used in describing parts of an expression. Instead of calling "sine" and "dy/dx" concepts, it's more useful, IMO, to call them what they are: trig function and derivative, respectively.

But if I assume a Trigonometric Equation like this.
y = 4 sin(x) + 4 cos2x(x)

1. What is sine called which has coefficient of '4'?
2. What is 'x' called which is seen in first term and second term of the equation?
3. What is 'y'?
4. What do I Google to find the names of the elements associated with any equation?
5. Are there any more names that are used for the elements of any equation when I talk mathematics?

In response to this question you have in post #1.
1. There is not a special name that I am aware of.
2. x is the independent variable.
3. y is the dependent variable. Its value depends on the value of x.
4. For the questions you're asking, there probably aren't very many special names, so trying to find them on the web will probably be fruitless. However, you might look up the terms "monomial" and "polynomial," which describe expressions made up of one term (monomial) or more than one term (polynomial).
5. Look up the terms that are used in basic algebra, such as monomial, binomial, trinomial, polynomial. The taxonomy doesn't usually go much beyond this.

 

[pairofstrings]

Thank you for the response.

What's the point of calling, say, Permutation and Combination a concept?

What should it be called?

 

[jbriggs444]

What should it be called?

What is the point of calling them anything? Perhaps Shakespeare said it best...

What's in a name? That which we call a rose
By any other name would smell as sweet

 

[pairofstrings]

I think humanity is moving forward because of the act of giving names. This statement can be explained much better by looking at why we give version numbers to a software.

Like: We make a statement and say something about it. Then we make another statement which is better than before and again we say something about it and then we make a statement and say something about it. This cycle continues, I think. This or if someone have secretly proved P versus NP to be true?

 

[Mark44]

I think humanity is moving forward because of the act of giving names.
This statement can be explained much better by looking at why we give version numbers to a software.
Like: We make a statement and say something about it. Then we make another statement which is better than before and again we say something about it and then we make a statement and say something about it. This cycle continues, I think. This or if someone have secretly proved P versus NP to be true?

In light of your original question, your comment here doesn't make much sense. You seem to be focussed on a taxonomy that doesn't exist because it isn't needed.

As you have been told by several members in this thread, much of what you're asking about really doesn't matter, and does nothing to "move humanity forward."

Since your question has been asked and answered, it seems this thread has run its course.