# The Naked Scientists Forum

### Author Topic: Trigonometry and Relativity  (Read 1671 times)

#### jeffreyH

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##### Trigonometry and Relativity
« on: 04/09/2016 14:40:29 »
Inspired by David Cooper I have put together the following. The range 0 to 1 relates directly to the sine and cosine functions within the range 0 to π/2 radians. This range can be used to represent the ration v/c that shows up as the ratio of squares in the gamma function.

So that if

θ = arcsin v/c

and

α = cos θ
β = sec θ

then length contraction l  and time dilation t can be expressed as

l = Lα
t = Tβ

where L = proper length and T = proper time. If we set c = 1 then we can relate this to the unit circle. This applies to quadrant I where all values are positive. Investigation of the angles involved and what they might imply is ongoing.

#### GoC

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##### Re: Trigonometry and Relativity
« Reply #1 on: 04/09/2016 19:23:31 »
If you believe in Relativity and follow light being independent of the source it becomes obvious that all views are from the past. At relativistic speeds you move away from the image created faster and now view the image of the past at an angle different from perpendicular. The image contracts by the vector angle of the observer receiving the image. What could be simpler. Contraction is visual and not physical!

#### jeffreyH

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##### Re: Trigonometry and Relativity
« Reply #2 on: 04/09/2016 21:06:07 »
The only way that light is related to the above is via the speed of light (c) used in the ratio v/c. Nowhere do I mention photons?

#### GoC

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##### Re: Trigonometry and Relativity
« Reply #3 on: 04/09/2016 22:08:08 »
If your not relating those angles to SR relativity than you are just doing an exercise in trig. If there was no photons we would have no proper length to discuss. I felt it was implied. Forgive me if I was incorrect.

#### jeffreyH

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##### Re: Trigonometry and Relativity
« Reply #4 on: 04/09/2016 22:16:31 »
It would be better to have maxima along the positive x axis and minima perpendicular at 90 degrees.

So that

θ = arccos v/c

and

α = sin θ
β = csc θ

In which case we can attempt to map this positions in the gravitational field at varying potentials right up to the photon sphere and the event horizon of a Schwarzschild black hole.

#### jeffreyH

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##### Re: Trigonometry and Relativity
« Reply #5 on: 04/09/2016 22:19:30 »
There, now I've mentioned photons.

#### jeffreyH

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##### Re: Trigonometry and Relativity
« Reply #6 on: 05/09/2016 08:26:52 »
For related equations please see

https://www.av8n.com/physics/spacetime-trig.htm

#### Thebox

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##### Re: Trigonometry and Relativity
« Reply #7 on: 05/09/2016 10:15:20 »
Inspired by David Cooper I have put together the following. The range 0 to 1 relates directly to the sine and cosine functions within the range 0 to π/2 radians. This range can be used to represent the ration v/c that shows up as the ratio of squares in the gamma function.

So that if

θ = arcsin v/c

and

α = cos θ
β = sec θ

then length contraction l  and time dilation t can be expressed as

l = Lα
t = Tβ

where L = proper length and T = proper time. If we set c = 1 then we can relate this to the unit circle. This applies to quadrant I where all values are positive. Investigation of the angles involved and what they might imply is ongoing.

It is interesting how ''alien'' something looks when a person  like myself does not understand it.

Can you first explain cos and sin in simple terms?

#### jeffreyH

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##### Re: Trigonometry and Relativity
« Reply #8 on: 05/09/2016 12:04:34 »
Inspired by David Cooper I have put together the following. The range 0 to 1 relates directly to the sine and cosine functions within the range 0 to π/2 radians. This range can be used to represent the ration v/c that shows up as the ratio of squares in the gamma function.

So that if

θ = arcsin v/c

and

α = cos θ
β = sec θ

then length contraction l  and time dilation t can be expressed as

l = Lα
t = Tβ

where L = proper length and T = proper time. If we set c = 1 then we can relate this to the unit circle. This applies to quadrant I where all values are positive. Investigation of the angles involved and what they might imply is ongoing.

It is interesting how ''alien'' something looks when a person  like myself does not understand it.

Can you first explain cos and sin in simple terms?

https://en.m.wikipedia.org/wiki/Trigonometric_functions

#### Thebox

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##### Re: Trigonometry and Relativity
« Reply #9 on: 07/09/2016 06:58:11 »
Inspired by David Cooper I have put together the following. The range 0 to 1 relates directly to the sine and cosine functions within the range 0 to π/2 radians. This range can be used to represent the ration v/c that shows up as the ratio of squares in the gamma function.

So that if

θ = arcsin v/c

and

α = cos θ
β = sec θ

then length contraction l  and time dilation t can be expressed as

l = Lα
t = Tβ

where L = proper length and T = proper time. If we set c = 1 then we can relate this to the unit circle. This applies to quadrant I where all values are positive. Investigation of the angles involved and what they might imply is ongoing.

It is interesting how ''alien'' something looks when a person  like myself does not understand it.

Can you first explain cos and sin in simple terms?

https://en.m.wikipedia.org/wiki/Trigonometric_functions

so x=cos  ?

y=sin?

tan= angle?

#### jeffreyH

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##### Re: Trigonometry and Relativity
« Reply #10 on: 07/09/2016 08:41:07 »
Careful now people might actually get the impression that you know this stuff. That can't possibly be true.

#### Thebox

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##### Re: Trigonometry and Relativity
« Reply #11 on: 07/09/2016 08:49:42 »
Careful now people might actually get the impression that you know this stuff. That can't possibly be true.

I don't know this although I have glanced cos and sin before.

I have no  idea why we call it cos and sin when x and y would seem to do, why do we rename X and Y ?

added- why can't we just overlay a protractor?

#### Colin2B

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##### Re: Trigonometry and Relativity
« Reply #12 on: 07/09/2016 09:30:03 »
I don't know this although I have glanced cos and sin before.

I have no  idea why we call it cos and sin when x and y would seem to do, why do we rename X and Y ?
You are not just renaming them. You are using them in a formula, so you can show how x or y varies with the value of different angles, the protractor won't do that.

Have a real look at the link Jeff gave, not just a glance. This is one of the fundamentals of maths and it's worth understanding.
Note I say understanding, not just learning by rote.

PS you can find some good maths textbooks in German if that helps

#### Thebox

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##### Re: Trigonometry and Relativity
« Reply #13 on: 07/09/2016 16:57:44 »
I don't know this although I have glanced cos and sin before.

I have no  idea why we call it cos and sin when x and y would seem to do, why do we rename X and Y ?
You are not just renaming them. You are using them in a formula, so you can show how x or y varies with the value of different angles, the protractor won't do that.

Have a real look at the link Jeff gave, not just a glance. This is one of the fundamentals of maths and it's worth understanding.
Note I say understanding, not just learning by rote.

PS you can find some good maths textbooks in German if that helps

I am reading it and have read it, do not yet understand  it .

Is tan=x,y?

edit - sorry ignore the tan =x,y , is X,Y equal to 90 degrees?  and then tan is worked within this?

added - I drew this so far?

Hope I am not spoiling your thread Jeff, I am trying to understand what you are discussing.

« Last Edit: 07/09/2016 17:17:01 by Thebox »

#### jeffreyH

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##### Re: Trigonometry and Relativity
« Reply #14 on: 07/09/2016 18:47:12 »
Think of a triangle with all 3 sides the same length. Two of the sides will form a right angle of 90 degrees (pi/2 radians). Sine, cosine and tangent can be described by the 'word' sohcahtoa. This stands for sine is opposite side divided by adjacent side, cosine is adjacent side divided by the hypotenuse and tangent is the opposite side divided by the adjacent side. Let me know when you have worked out why this is true. And no nonsense.

#### alancalverd

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##### Re: Trigonometry and Relativity
« Reply #15 on: 07/09/2016 23:31:50 »
Quote
Think of a triangle with all 3 sides the same length. Two of the sides will form a right angle of 90 degrees (pi/2 radians).

Oh no they won't!

#### jeffreyH

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##### Re: Trigonometry and Relativity
« Reply #16 on: 08/09/2016 00:56:46 »
Quote
Think of a triangle with all 3 sides the same length. Two of the sides will form a right angle of 90 degrees (pi/2 radians).

Oh no they won't!

Yes like what Alan said. No right angle. All the angles are ?? degrees. Hint they add up to 180. Tough crowd!

#### jeffreyH

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##### Re: Trigonometry and Relativity
« Reply #17 on: 08/09/2016 00:58:24 »
P.S. There are 3 angles.

#### Thebox

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##### Re: Trigonometry and Relativity
« Reply #18 on: 08/09/2016 08:14:02 »
P.S. There are 3 angles.

Now I am confused you seem to be arguing with each other about a triangle.

A triangle has 3 ''sides''

If cos=sin we have one 90 degree and two acute angles, if a triangle is an equilateral triangle, there is no 90 degree and 3 acutes?

#### jeffreyH

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##### Re: Trigonometry and Relativity
« Reply #19 on: 08/09/2016 08:22:38 »
P.S. There are 3 angles.

Now I am confused you seem to be arguing with each other about a triangle.

A triangle has 3 ''sides''

If cos=sin we have one 90 degree and two acute angles, if a triangle is an equilateral triangle, there is no 90 degree and 3 acutes?

Sorry for confusing you. Yes there are 3 acute angles in an equilateral. Keep on going. It's worth the effort.

#### Thebox

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##### Re: Trigonometry and Relativity
« Reply #20 on: 08/09/2016 08:31:21 »
P.S. There are 3 angles.

Now I am confused you seem to be arguing with each other about a triangle.

A triangle has 3 ''sides''

If cos=sin we have one 90 degree and two acute angles, if a triangle is an equilateral triangle, there is no 90 degree and 3 acutes?

Sorry for confusing you. Yes there are 3 acute angles in an equilateral. Keep on going. It's worth the effort.

The easy way would  be to ''draw'' a square around the triangle and calculate within the square, however I do know that is not your way, so how do we work out the acute angles, I don't understand the formula as yet.

And how do we determine which way up the triangle is to apply cos and sin?

#### alancalverd

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##### Re: Trigonometry and Relativity
« Reply #21 on: 08/09/2016 10:13:19 »
The only time cos x  = sin x is when x = pi/4 or 5pi/4.

Wake up, guys, this stuff is pre-'O' level - in fact only just post-11-plus!

#### Thebox

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##### Re: Trigonometry and Relativity
« Reply #22 on: 08/09/2016 10:15:57 »
The only time cos x  = sin x is when x = pi/4 or 5pi/4.

Wake up, guys, this stuff is pre-'O' level - in fact only just post-11-plus!

Its only easy if you know the answer Alan, I have no idea about this subject, I am has fresh as a junior when it comes to this.

pi/4  I dont follow that?

If cos is ten miles long and sin is ten miles long, then surely cos=sin?  or am I confusing this with calculus?

« Last Edit: 08/09/2016 10:29:33 by Thebox »

#### alancalverd

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##### Re: Trigonometry and Relativity
« Reply #23 on: 08/09/2016 13:10:00 »
I strongly advise you to learn some elementary maths before paddling in the waters of science. Maths is the language of physics just as German is the language of Germany.

#### Thebox

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##### Re: Trigonometry and Relativity
« Reply #24 on: 08/09/2016 13:15:02 »
I strongly advise you to learn some elementary maths before paddling in the waters of science. Maths is the language of physics just as German is the language of Germany.

I thought trig was maths?  that I have ventured into,  I know what  pi is and the divide by 4, but I dont get how that relates, but yes perhaps I should start with some maths less complex looking.

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##### Re: Trigonometry and Relativity
« Reply #24 on: 08/09/2016 13:15:02 »