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#1 2005-12-24 07:38:30
- krassi_holmz
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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.
#2 2005-12-24 07:40:56
- krassi_holmz
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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.
#3 2005-12-24 07:43:51
- krassi_holmz
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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.
#4 2005-12-24 08:06:01
- krassi_holmz
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Re: Trigonometric function with half-square graph?
Oops...
Just ArcCos[Sin[x]] makes square.
IPBLE: Increasing Performance By Lowering Expectations.
#5 2005-12-24 16:30:56
- John E. Franklin
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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 (2005-12-24 16:40:19)
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#6 2006-01-12 09:30:48
- God
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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