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## #1 2005-12-23 08:38:30

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Trigonometric function with half-square graph?

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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## #2 2005-12-23 08:40:56

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: Trigonometric function with half-square graph?

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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## #3 2005-12-23 08:43:51

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: Trigonometric function with half-square graph?

Sq[x] is periodic with period Pi.
I've started making some pictures.

IPBLE:  Increasing Performance By Lowering Expectations.

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## #4 2005-12-23 09:06:01

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: Trigonometric function with half-square graph?

Oops...
Just ArcCos[Sin[x]] makes square.

IPBLE:  Increasing Performance By Lowering Expectations.

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## #5 2005-12-23 17:30:56

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Trigonometric function with half-square graph?

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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## #6 2006-01-11 10:30:48

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

### Re: Trigonometric function with half-square graph?

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

The parametric square = awesome

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