DimaMazin

Yes. If you know what is arcsine and arccosine then you should understand what is arc of unit circle. Arc of definition is part of unit circle.

Coordinates of point of definition: x = ( a - sin(a))*cos(a/2) / [cos(a/2)*(a - sin(a)) - sin(a/2)*(1 - cos(a))] y = sin(a/2)*(a - sin(a)) / [cos(a/2)*(a - sin(a)) - sin(a/2)*(1 - cos(a))] Pi/(2a) = sin(a/2)*(a - sin(a)+1 - cos(a))/[sin(a)*cos(a/2)*(a - sin(a))+(1 - cos(a))*((sin(a/2) - cos(a/2)*(a - sin(a))+sin(a/2)(1 - cos(a)))]

Excuse me Studiot. I just showed how it can define unknown angle when arc of definition is known and coordinates of point of definition are known. But if your computer can solve very complex equation then please solve this one: a is arc of definition ( rad) Pi/(2a) = sin(a/2)*(a - sin(a)+1 - cos(a))/[sin(a)*cos(a/2)*(a - sin(a))+(1 - cos(a))*((sin(a/2) - cos(a/2)*(a - sin(a))+sin(a/2)(1 - cos(a))]

Sine is known there. I defined angle.

Length of arc of definition is a coordinates of point of definition(cross point of 5 lines) are (x1 ; y1) Length of chord is 2sin(a/2) Equation of chord is y=(sin(a)*x - sin(a))/(cos(a) - 1) For example we know sin and cos of unknown angle Let's define unknown angle : coordinates of point of unknown angle on arc are (cos;sin) Then draw straight line through points (cos;sin) and (x1;y1) Equation of the line is: y=(y1 - sin)*x/(x1 - cos)+sin - (y1 - sin)*cos/(x1 - cos) Cross point of the line and chord has coordinates (x ' ; y' ) We know equations of the line and the chord therefore we can define x' (it is complex) (1 - x')/(1 - cos(a))= part of divided chord / chord = unknown angle / a unknown angle = a*(1 - x')/(1 - cos(a))

Yes and proportional divisions can be any , but coordinates of cross point should be constant.

Draw unit circle x2+y2=1 Mark angle 166 degrees or 168 degrees . Divide this angle for 6 equal parts. Draw chord of this arc(angle). Divide the chord for 6 equal parts. Draw straight line through 2 points , one of which divides arc for 1/6 part and 5/6 parts, another divides chord for 1/6 part and 5/6 parts. Then draw second straight line through 2 next points, one of which divides arc for 2/6 and 4/6 parts, another divides chord for 2/6 and 4/6 parts. Draw next straight lines through corresponding next points. If your arc is arc of definition then all these straight lines cross in one point of definition trigonometric functions and angles. If you know angle then you can define sine&cosine. If you know sine&cosine then you can define angle because you know coordinates of point of cross straight lines .

Arc is angle(rad). I made some explore. If it exists then rather it is between 5/6 Pi and 17/18 Pi .

I should not louse time. I should define arc of definition.

Sine and cosine are coordinates of concrete point. They cannot be approximate. Otherwise how can you define equation of straight line which crosses this point?

Correct definition of trigonometric functions should make exact value for any specific angle. Concretely you don't need such definition. Thank you for honest answer.

What is exact sin(Pi/4)=21/2/2 or sin(Pi/4)=0.7071067812 ? Can you define sine of any angle with exponents?

I didn't like approximate definitions of trigonometric functions (it was about 34 years ago). Then I made speculation that side of angle (if angle is less or equal to Pi/2 rad) proportionally divides arc Pi/2 and its chord (21/2). Then my math teacher corrected me with her speculation that there is especial arc in which if to connect any two points of proportional division of this arc and its chord by straight line and to connect any two points of any another proportional division of this arc and its chord by another straight line , then the straight lines cross in one point of definition of trigonometric functions and angles(arcs). Is there any prize for exact definition of trigonometric functions and angles ?

Frame of escaping traveler and frame of arriving the same traveler have slower time relative each other than relative to home frame. Therefore traveled clock shows less time than home clock at meeting.

Simultaneity is ratio of quantities of changes between determinations of distances and positions.

We can not use that method when we don't know unknown phenomenon with time. Therefore firstly we should define what is unknown then maybe it is a time. I think we don't know quantity of exchange of energy through space . Then t = q / Er t is time q is quantity of exchange of energy through space Er is relativistic energy

What is wrong again?

All my ideas are wrong. I think reality is simpler. Orbits of electrons and of particles in atom are increased due to increased space in gravitation. Therefore particles should more travel for a creation and a change of events . Later changes cause later photon radiation in atomic clock of gravitational observer.

Next idea: Motionless mass has an energy for creation of own time, part of which is kinetic energy in another reference frame. Also mass has an energy for support of gravitation. When mass is falling in gravitation it firstly loses part of energy for creation own time and gets acceleration. When the mass is stopped in gravitation it has less energy for creation of own time and more energy for support of gravitation.

Change of position of relativistic energy with mass and without mass creates change of time. My formula shows it.

All humanity is stopped.

Well. I am very wrong earlier. Let's consider next idea. Er=gamma*mc2 Er=mc3/(c2-v2)1/2 (mc3/Er)2=c2-v2 v2=c2-m2c6/Er2 v=c(Er2 - m2c4)1/2/Er dt=dx/v dt=Erdx/(c(Er2 - m2c4)1/2 I have made formula of dt definition.

Today we can lose momentum because p = Er*v/c2

Er is relativistic energy https://en.wikipedia.org/wiki/Energy–momentum_relation Er2 = m2c4+p2c2 Er2= m2c4 +m2v2c4/(c2-v2) Er2=m2c4+m2dx2c4/(c2t2-dx2) Er2c2t2 - Er2dx2=m2c6t2 - m2c4dx2+m2c4dx2 t2=Er2dx2/(Er2c2 - m2c6) t=Erdx/(c(Er2 -m2c4)1/2 t=Erdx/(c(p2c2+m2c4 - m2c4)1/2 t=Erdx/(pc2)

At all t = Er* dx/(|p| c2) Moved relativistic energy exists in motionless object