I am too lazy to make mine white (CaptainBlank do that for me). (Talk about a dictator who breaks his own rules)

Okay, the correct answer was,
|y|<=sin(sin(sin(sin(1))))
Anyone understand why?

I have a formal treatment of this if anyone is interested?
So how you like my puzzle, fun, easy, too hard?

__________________

To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.


"Democracy has proved only that the best way to gain power
over people is to assure the people that they are ruling
themselves. Once they believe that, they make wonderfully
submissive slaves." - Joseph Sobran

The extension to this PoW is still unanswered.

I will repeat it in case people did not notice that someone had actually
asked this.

What is the range of:

f(z) = sin(sin(sin(sin(sin(z)))))

when the domain is C the set of all complex numbers?

RonL

__________________
Truth does not change because it is, or is not, believed by a majority of the people.

Giordano Bruno

It was too easy I'm afraid. To the extent that I knew the answer straight away but was struggling to find a way of writing it exactly which apparently isn't possible.

__________________
Vaiyo A-O
A Home Va Ya Ray
Vaiyo A-Rah
Jerhume Brunnen G
Vaiyo A-Rah
Jerhume Brunnen G

That's it? I spent all those hours trying (and failing) to come up with some exact multiple of pi for the limits of the domain and you're leaving the answer like that?? (grumbles) Heck, I had THAT answer within 30 seconds of starting the problem! (I had thought that expressing the exact answer in another form was the meat of the problem. )

Me thinks that if the answer is going to be in that form the problem was a bit too easy.

-Dan

__________________
Got a Physics question? Come on over to
To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.

To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.


"I must not fear. Fear is the mind killer. Fear is the little death that brings total obliteration. I will face my fear. I will permit it to pass over me and through me. And when it has gone I will turn the inner eye to see its path. Where the fear has gone there will be nothing. Only I will remain." - The Litany Against Fear, "Dune" by Frank Herbert

Find the maximum of by setting the derivative equal to zero:



One obvious solution is because .

So either the maximum or minimum occur at

Since is even, its range is .

Which is the same as .

No one seems interested in this so I will post the answer:

sin(z) is entire, so the image of C under sin is C, so the range of f(z) is C

RonL

__________________
Truth does not change because it is, or is not, believed by a majority of the people.

Giordano Bruno