Author 
Topic: sin cos and cos sin (Read 10890 times) 

BNC
Uberpuzzler
Gender:
Posts: 1732


Re: sin cos and cos sin
« Reply #1 on: Jun 12^{th}, 2004, 5:56am » 
Quote Modify

which goes to show that computer proofs have thei place: "solving" it graphically us very easy...


IP Logged 
How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]



Eigenray
wu::riddles Moderator Uberpuzzler
Gender:
Posts: 1948


Re: sin cos and cos sin
« Reply #2 on: Jun 12^{th}, 2004, 10:28pm » 
Quote Modify

First, we only need to consider x in [[pi],[pi]] by periodicity. Second, because sin(cos(x)) and cos(sin(x)) are both even, we only need to consider x in [0, [pi]]. If x is in [[pi]/2, [pi]], then sin(cos(x)) [le] sin(0) = 0 < cos(1) [le] cos(sin(x)). So now suppose 0 < x < [pi]/2, and suppose sin(cos(x))=cos(sin(x)). Let y = sin(x), z = cos(x), so that 0 < y,z < 1 sin(z) = cos(y) = sin(y+[pi]/2), which means z = y+[pi]/2 +2n[pi], or z = [pi](y+[pi]/2) + 2n[pi], for some integer n. In the first case, 1 < zy = [pi]/2 + 2n[pi] < 1, which is impossible. In the second case, 0 < y+z = [pi]/2 + 2n[pi] < 2, which is possible only for n=0, which means: [pi]/2 = y+z = sin(x)+cos(x) = [sqrt]2 sin(x+[pi]/4), which is impossible because [pi]/2 > [sqrt]2. And by the intermediate value theorem, if the function sin(cos(x))cos(sin(x)) is never 0, it's either always positive or always negative. So to answer the question, cos(sin(x)).


IP Logged 



srn437
Newbie
the dark lord rises again....
Posts: 1


Re: sin cos and cos sin
« Reply #3 on: Sep 16^{th}, 2007, 4:16pm » 
Quote Modify

Also, cos(x)>sin(x). But what about sin^{2}(x)+cos^{2}(x) or cos^{4}(x) + sin^{4}(x) +2sin^{2}(x)(cos^{2}(x))?

« Last Edit: Sep 16^{th}, 2007, 4:25pm by srn437 » 
IP Logged 



ThudnBlunder
wu::riddles Moderator Uberpuzzler
The dewdrop slides into the shining Sea
Gender:
Posts: 4489


Re: sin cos and cos sin
« Reply #4 on: Sep 16^{th}, 2007, 5:13pm » 
Quote Modify

on Sep 16^{th}, 2007, 4:16pm, srn347 wrote:Also, cos(x)>sin(x). But what about sin^{2}(x)+cos^{2}(x) ? 
 cos(pi/3) < sin(pi/3) sin^{2}x + cos^{2}x = 1


IP Logged 
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.



srn437
Newbie
the dark lord rises again....
Posts: 1


Re: sin cos and cos sin
« Reply #5 on: Sep 16^{th}, 2007, 5:51pm » 
Quote Modify

Check again. My calculator says otherwise about the pi/3 thing. That sin^{2}(x)+cos^{2}(x)=1 thing is true and in the question I asked, it is useful in finding the answer.


IP Logged 



ThudnBlunder
wu::riddles Moderator Uberpuzzler
The dewdrop slides into the shining Sea
Gender:
Posts: 4489


Re: sin cos and cos sin
« Reply #6 on: Sep 16^{th}, 2007, 6:01pm » 
Quote Modify

on Sep 16^{th}, 2007, 5:51pm, srn347 wrote:Check again. My calculator says otherwise about the pi/3 thing. 
 Change your setting from Degrees to Radians and we'll be on the same page, kid.


IP Logged 
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.



srn437
Newbie
the dark lord rises again....
Posts: 1


Re: sin cos and cos sin
« Reply #7 on: Sep 16^{th}, 2007, 6:29pm » 
Quote Modify

It isn't that kind of calculator, but ok. How is that though? Shouldn't the series be the same? What about the other question I asked(which is higher:sin^{2}(x)+cos^{2}(x) or sin^{4}(x)+cos^{4}(x)+2sin^{2}(x)cos^{2}(x))?


IP Logged 



Aryabhatta
Uberpuzzler
Gender:
Posts: 1327


Re: sin cos and cos sin
« Reply #8 on: Sep 16^{th}, 2007, 9:04pm » 
Quote Modify

on Sep 16^{th}, 2007, 6:29pm, srn347 wrote: What about the other question I asked(which is higher:sin^{2}(x)+cos^{2}(x) or sin^{4}(x)+cos^{4}(x)+2sin^{2}(x)cos^{2}(x))? 
 Do you really think such a trivial question should be in medium? One is the square of the other and both are 1. Also, please don't use existing threads to post your questions, create new ones instead (and in the appropriate forum).


IP Logged 



srn437
Newbie
the dark lord rises again....
Posts: 1


Re: sin cos and cos sin
« Reply #9 on: Sep 17^{th}, 2007, 6:25am » 
Quote Modify

Once the question on a thread has been answered correctly, what else is there to do other than ask another question. Your answer was correct though.


IP Logged 



Barukh
Uberpuzzler
Gender:
Posts: 2276


Re: sin cos and cos sin
« Reply #10 on: Sep 17^{th}, 2007, 7:58am » 
Quote Modify

on Sep 17^{th}, 2007, 6:25am, srn347 wrote:Once the question on a thread has been answered correctly, what else is there to do other than ask another question 
 Incorrect. Please start a different thread if you want to ask a different question. You may supply a link to a relevant existing thread, if you wish.


IP Logged 



towr
wu::riddles Moderator Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13276


Re: sin cos and cos sin
« Reply #11 on: Sep 17^{th}, 2007, 8:00am » 
Quote Modify

on Sep 17^{th}, 2007, 6:25am, srn347 wrote:Once the question on a thread has been answered correctly, what else is there to do other than ask another question. 
 If the new question is relevant to the topic, that's fine. Otherwise, it's better to leave the thread alone and ask the question in its own (and properly named) thread, so people that are interested in finding it can find it.


IP Logged 
Wikipedia, Google, Mathworld, Integer sequence DB



srn437
Newbie
the dark lord rises again....
Posts: 1


Re: sin cos and cos sin
« Reply #12 on: Sep 17^{th}, 2007, 5:59pm » 
Quote Modify

The new question was relevant. What is radiens anyway?


IP Logged 



ThudnBlunder
wu::riddles Moderator Uberpuzzler
The dewdrop slides into the shining Sea
Gender:
Posts: 4489


Re: sin cos and cos sin
« Reply #13 on: Sep 17^{th}, 2007, 7:23pm » 
Quote Modify

on Sep 17^{th}, 2007, 5:59pm, srn347 wrote: All you paid was the looking price. Lessons are extra.  Edward G. Robinson One minute you are telling professional mathematicians, engineers, and computer scientists what's what, and the next minute you are asking what 'radiens' are.

« Last Edit: Sep 18^{th}, 2007, 9:13am by ThudnBlunder » 
IP Logged 
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.



Sameer
Uberpuzzler
Pie = pi * e
Gender:
Posts: 1258


Re: sin cos and cos sin
« Reply #14 on: Sep 17^{th}, 2007, 8:08pm » 
Quote Modify

Apparently a trigonometry class is in order!! Whatever happened to ignoring?


IP Logged 
"Obvious" is the most dangerous word in mathematics. Bell, Eric Temple
Proof is an idol before which the mathematician tortures himself. Sir Arthur Eddington, quoted in Bridges to Infinity



Aryabhatta
Uberpuzzler
Gender:
Posts: 1327


Re: sin cos and cos sin
« Reply #15 on: Sep 17^{th}, 2007, 8:17pm » 
Quote Modify

on Sep 17^{th}, 2007, 8:08pm, Sameer wrote:Whatever happened to ignoring? 
 I tried, but as there always seemed to be someone who responded, so I gave up.


IP Logged 



Aryabhatta
Uberpuzzler
Gender:
Posts: 1327


Re: sin cos and cos sin
« Reply #16 on: Sep 17^{th}, 2007, 8:19pm » 
Quote Modify

on Sep 17^{th}, 2007, 5:59pm, srn347 wrote:The new question was relevant. 
 How so? If your answer is "trignometry" and "sin and cos", it is a bunch of bullsh*t. The question you asked was not relevant and trivial to boot. You just polluted this thread. Sorry for the harsh words, but that is the truth.


IP Logged 



ThudnBlunder
wu::riddles Moderator Uberpuzzler
The dewdrop slides into the shining Sea
Gender:
Posts: 4489


Re: sin cos and cos sin
« Reply #17 on: Sep 17^{th}, 2007, 8:23pm » 
Quote Modify

on Sep 17^{th}, 2007, 8:08pm, Sameer wrote:Whatever happened to ignoring? 
 Ignore it is then.


IP Logged 
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.



Aryabhatta
Uberpuzzler
Gender:
Posts: 1327


Re: sin cos and cos sin
« Reply #18 on: Sep 17^{th}, 2007, 8:30pm » 
Quote Modify

on Sep 17^{th}, 2007, 8:23pm, ThudanBlunder wrote: Ignore it is then. 
 Sorry. I will start ignoring again.


IP Logged 



srn437
Newbie
the dark lord rises again....
Posts: 1


Re: sin cos and cos sin
« Reply #19 on: Sep 17^{th}, 2007, 8:40pm » 
Quote Modify

Can any of you give me a straight answer?! // resized fonts. Oversized fonts will not make people pay more attention to you. It is simply annoying. towr

« Last Edit: Sep 18^{th}, 2007, 12:21am by towr » 
IP Logged 



Sameer
Uberpuzzler
Pie = pi * e
Gender:
Posts: 1258


Re: sin cos and cos sin
« Reply #20 on: Sep 17^{th}, 2007, 8:45pm » 
Quote Modify

Come to think of this topic, Where is Nick nowadays? He is missing like Icarus...


IP Logged 
"Obvious" is the most dangerous word in mathematics. Bell, Eric Temple
Proof is an idol before which the mathematician tortures himself. Sir Arthur Eddington, quoted in Bridges to Infinity



srn437
Newbie
the dark lord rises again....
Posts: 1


Re: sin cos and cos sin
« Reply #21 on: Sep 17^{th}, 2007, 9:01pm » 
Quote Modify

I wonder...


IP Logged 



ima1trkpny
Senior Riddler
"Double click on 'Yes'... Hey!"
Gender:
Posts: 452


Re: sin cos and cos sin
« Reply #22 on: Sep 17^{th}, 2007, 9:15pm » 
Quote Modify

on Sep 17^{th}, 2007, 8:45pm, Sameer wrote:Come to think of this topic, Where is Nick nowadays? He is missing like Icarus... 
 Nick's last post was in Jan... he's been gone even longer than Icarus (maybe he just decided 4600 was a nice even number of posts? I did actually check cause I was worried and there was no sign of him in the Wichita obits... so I assume he is fine and possibly either just busy or as I said before really likes that number) Raven too has been missing for awhile...

« Last Edit: Sep 17^{th}, 2007, 9:16pm by ima1trkpny » 
IP Logged 
"The pessimist sees difficulty in every opportunity. The optimist sees the opportunity in every difficulty." Churchill



mikedagr8
Uberpuzzler
A rich man is one who is content; not wealthy.
Gender:
Posts: 1105


Re: sin cos and cos sin
« Reply #23 on: Sep 18^{th}, 2007, 12:30am » 
Quote Modify

Quote:Apparently a trigonometry class is in order!! 
 Hehe, just had a triple today. A radian is a measurement around a circle. Now for someone to have known calculus, YOU NEED TO KNOW THIS BACK TO FRONT!!! Luckily for me, I have just completed the topic, so I am well aware of what is required, you on the other hand, need to learn a few things srn347. The faster the better.


IP Logged 
"It's not that I'm correct, it's that you're just not correct, and so; I am right."  M.P.E.



SMQ
wu::riddles Moderator Uberpuzzler
Gender:
Posts: 2077


Re: sin cos and cos sin
« Reply #24 on: Sep 18^{th}, 2007, 6:10am » 
Quote Modify

on Sep 17^{th}, 2007, 8:40pm, srn347 wrote:Can any of you give me a straight answer?! 
 Sorry, we keep assuming you know how to use Wikipedia, Mathworld, or at least Google to answer simple questions for yourself. A radian is a measure of angle equal to the arc length of a corresponding segment of a circle with unit radius. Since the perimeter of a unit circle is 2, 360^{o} = 2 radians. SMQ


IP Logged 
SMQ



