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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

This thing is very amasing for me.

t∈[0, π]

x=ArcSin[Cos[t]]

y=ArcCos[Sin[t]]

What is the graphic plot of this parametric sequence?

Yes, this is a square!

And the function

y = ArcCos[Sin[ArcCos[Sin[x]]]]

is half square!

...Interesting...

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

If ArcCos[Sin[ArcCos[Sin[x]]]] = Sq[x] then I found interesting property:

Sq[Sq[x]]=Sq[x]!

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

Sq[x] is periodic with period Pi.

I've started making some pictures.

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

Oops...

Just ArcCos[Sin[x]] makes square.

IPBLE: Increasing Performance By Lowering Expectations.

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,565

If you don't restrict t, it makes sawtooth waves.

Wow, different sizes!! Nice discovery!

'Course I only did the y=stuff equations.

I don't understand combining both together yet.

...

Oh I think I'm getting the idea of the parametric stuff.

Neat concept. I never had heard of it before!

...

So for like normal functions,

x = t and y = f(x) equation.

But now it's all in terms of t, wow, really flexible.

Never would have thought of that idea.

*Last edited by John E. Franklin (2005-12-23 17:40:19)*

**igloo** **myrtilles** **fourmis**

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**God****Member**- Registered: 2005-08-25
- Posts: 59

I'm not really getting a square... at least not with the explicit equations.

The parametric square = awesome

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