Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

## #1 2005-12-24 07:38:30

krassi_holmz
Real Member

Offline

### 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
Real Member

Offline

### 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
Real Member

Offline

### 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
Real Member

Offline

### 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
Star Member

Offline

### 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)

Imagine for a moment that even an earthworm may possess a love of self and a love of others.

## #6 2006-01-12 09:30:48

God
Full Member

Offline

### 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