# How to define arc of definition?

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1 hour ago, DimaMazin said:

What will be  when ( Pi/infinity)*infinity ?

From usual definitions it would be $$\pi/\infty = 0$$ and $$0 \cdot \infty = 0,$$ so that means $$(\pi/\infty)\cdot \infty = 0.$$ But it seems you are trying to treat $$\infty$$ as if it were a natural number, and that has only small chance or working out. I do not think that you need to introduce $$\infty$$ in the first place anyway.

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On 4/10/2020 at 10:17 PM, taeto said:

From usual definitions it would be π/=0 and 0=0, so that means (π/)=0. But it seems you are trying to treat as if it were a natural number, and that has only small chance or working out. I do not think that you need to introduce in the first place anyway.

Let's consider that stupid rule instead of true science because it will appear again and again .

(Pi/million)*million=Pi

(Pi/billion)*billion=Pi

There is no trend to reduce result therefore so called scientists should prove that billion is not nearer to infinity than million.

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On 4/10/2020 at 3:16 PM, DimaMazin said:

Yes. Let's consider next thing:

Arc Pi -2 a   is divided for infinite quantity equal parts  and its chord is divided for infinite quantity of equal parts.The straight line intersects the nearest points of the divisions to its middle . The point on arc has coordinates([Pi-2a]/infinity ; 1), the point on chord has coordinates (cos(a)/infinity ; sin(a)). Their straight line intersects y axis in point(0; y1) . Increased side (Pi - 2a)/infinity of the triangle in infinite quantity of times on tangent in point(0 ; 1) creates new point on its edge with coordinates ([Pi - 2a] ; 1). Increased side cos(a)/infinity of the smaller triangle in infinite quantity times has edge point(cos(a) ; sin(a)). The new straight line of the new points intersects y axis in the same point (0 ; y1).

y1 = (2a - Pi*sin2(a)) / (2a*sin(a) - Pi*sin(a)+2a*cos(a))

Some similar thing we can make with edge points of the division. Then their derivative points lie on straight line which intersects y axis in point(0 ; y2) I did not make equation for y2.

But feature exists there :         y1 is lower than y2  when arc is bigger than Pi - 2a

and         y1 is upper than y2  when arc is smaller than Pi - 2a

It can prove that the arc of definition of trigonometric functions exists.

I mistaken there

y1=[sin(a)*(Pi - 2a) - 2cos(a)] / [Pi-2cos(a)-2a]

y2= [2sin(a)*cos(a)+2a - Pi ] / [2cos(a) - sin(a)*(Pi - 2a)]

Now everyone can define is any arc less or more than the arc of definition.

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