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So the complex number z is given as   $z=1-cos(2\theta)-isin(2\theta)$  And the question is to find the argument of z in terms of $\theta$.   So, I used the formula for calculating the argument of a complex number:  $arg(z)=arctan (\frac{sin(2\theta)}{1-cos(2\theta)})$  $=arctan (\frac{2sin\theta cos\theta}{1-(1-2sin^2\theta)})$  $=arctan (\frac{2sin\theta cos\theta}{2sin^2\theta})$  $=arctan (\frac{cos\theta}{sin\theta})$  $=arctan (cot\theta)$  $=arctan (tan(\frac{\pi}{2}-\theta))$  $=\frac{\pi}{2}-\theta$  But apparently the answer is $\theta-\frac{\pi}{2}$.  Where might have I gone wrong?  Edit: the domain given in the question for $\theta$ was $0≤\theta≤\pi$ I am stuck with the following problem.     Prove that $$\limsup_{n \to \infty} (a_n+b_n) \le \limsup_{n \to \infty} a_n + \limsup_{n \to \infty} b_n$$   I was thinking of using the triangle inequality saying $$|a_n + b_n| \le |a_n| + |b_n|$$ but the problem is not about absolute values of the sequence.  Intuitively it's clear that this is true because $a_n$ and $b_n$ can "reduce each others magnitude" if they have opposite signs, but I cannot express that algebraically...  Can someone help me out ? text processing rows to columns for a block How to trigger a check for updates in Firefox programatically or from a command line? Is there a command line switch for firefox.exe or an "about:" URL that will either force an update check or at least display the Help/About dialog, which checks for updates and tells if you're running the latest version?    One site claimed that the "about:" URL was the same as menu Help -> About, but it's not.  I built a program to automate the updating of various programs on my machine, and most programs have command line tools for checking for updates. Windows update has wuauclt.exe, Java has jucheck.exe. For some applications, I can even automate the interface, but it's difficult in Firefox, because the main window title is unpredictable (it depends on which web page is active), and all Firefox windows seem to use the exact same window class name. I'm thinking of following some kind of education in physics online. I have a master degree in Computer Science and have reasonable good knowledge in physics. I would like a program of 1-2 years and I'm more interested in particle physics.   Is there any good online program that offer something similar? "Where" in careers' search seems to be broken Let's say I want to find a company in Ontario, Canada. Ok, I navigate to company pages and type ON, Canada to Where in search:        but there are no companies in there. So why if I type just Canada it finds companies in ontario; and if I type specific area (ON, CA)  it doesn't find anything ? How do I deal with a compromised server? This is a  about Server Security - Responding to Breach Events (Hacking)   See Also:                  Canonical Version I suspect that one or more of my servers is compromised by a hacker, virus, or other mechanism:   What are my first steps? When I arrive on site should I disconnect the server, preserve "evidence", are there other initial considerations? How do I go about getting services back online? How do I prevent the same thing from happening immediately again? Are there best practices or methodologies for learning from this incident? If I wanted to put a Incident Response Plan together, where would I start? Should this be part of my Disaster Recovery or Business Continuity Planning?   Original Version       2011.01.02 - I'm on my way into work at 9.30 p.m. on a Sunday because our server has been compromised somehow and was resulting in a    attack on our provider. The servers access to the Internet   has been shut down which means over 5-600 of our clients sites are now   down. Now this could be an FTP hack, or some weakness in code   somewhere. I'm not sure till I get there.      How can I track this down quickly? We're in for a whole lot of   litigation if I don't get the server back up ASAP. Any help is   appreciated. We are running Open SUSE 11.0.            2011.01.03 - Thanks to everyone for your help. Luckily I WASN'T the only person responsible for this server, just the nearest. We managed   to resolve this problem, although it may not apply to many others in a   different situation. I'll detail what we did.      We unplugged the server from the net. It was performing (attempting to   perform) a Denial Of Service attack on another server in Indonesia,   and the guilty party was also based there.      We firstly tried to identify where on the server this was coming from,   considering we have over 500 sites on the server, we expected to be   moonlighting for some time. However, with SSH access still, we ran a   command to find all files edited or created in the time the attacks   started. Luckily, the offending file was created over the winter   holidays which meant that not many other files were created on the   server at that time.      We were then able to identify the offending file which was inside the   uploaded images folder within a  website.      After a short cigarette break we concluded that, due to the files   location, it must have been uploaded via a file upload facility that   was inadequetly secured. After some googling, we found that there was   a security vulnerability that allowed files to be uploaded, within the   ZenCart admin panel, for a picture for a record company. (The section   that it never really even used), posting this form just uploaded any   file, it did not check the extension of the file, and didn't even   check to see if the user was logged in.      This meant that any files could be uploaded, including a PHP file for   the attack. We secured the vulnerability with ZenCart on the infected   site, and removed the offending files.      The job was done, and I was home for 2 a.m.            The Moral   - Always apply security patches for ZenCart, or any other CMS system for that matter. As when security updates are released, the whole   world is made aware of the vulnerability.   - Always do backups, and backup your backups.   - Employ or arrange for someone that will be there in times like these. To prevent anyone from relying on a panicy post on Server   Fault. “The group of fifty people {is / are} going to arrive Thursday” - which is preferred? Isn't the following sentence grammatically correct?     The group of fifty people are going to arrive Thursday.   What's wrong with it? Someone said it should be      The group of fifty people is going to arrive Thursday.   Why? People is plural so why is people is better than people are? How to sort lines by float number I've such a file:  name: xxx --- time: 5.4 seconds name: yyy --- time: 3.2 seconds name: zzz --- time: 6.4 seconds ...   Now I want to sort this file by these float numbers to generate a new file as below:  name: yyy --- time: 3.2 seconds name: xxx --- time: 5.4 seconds name: zzz --- time: 6.4 seconds ...   I've tried the command awk '{print $5}' myfile | sort -g but this will show me ONLY the float numbers. Looking for sci-fi short story anthology with a particular story of an Earth/Mars war children inheriting the surface I read this in the early to mid 80's.  It was a textbook sized hardcover anthology with color illustrations throughout.  Each story had a few images, some were full page illustrations.  The particular story I remember the most involved Earth survivors living underground.  Robots controlled the war from the surface.  A teenage girl and boy decided to sneak away to the surface as no one had been up there in a long time.  The kids discover greenery and a healthy environment, with rusted robot guardians.  The robots had been keeping the humans fooled that the war was still going on, and had kept them under the surface.  Mars had been wiped out from nearly the first volleys of missiles.    The robots judge the teenagers as worthy and let them remain on the surface.  The kids had silver jumpsuits that dissolved when they got wet.  The robot illustrations were blocky, almost weathered stone-like statues.  They had nearly spherical feet and square simple heads.  The faces had eyes and simple mouths.  -edit- The robots were similar in shape to the one in this picture, but smoother, and no arms.  The illustrations with them had the robots being several stories tall.  I kind of remember that the kids emerged from the belly of one or something like that. I tried to choose a answer for a question on SA and someone immediately answered with the correct response. I try to click the check box and it says wait 2 min. I keep clicking until it changes from 2 min to 1 min. I wait 60 seconds on my watch and click again and it says please wait 59 seconds.  The 2 minute mark should have said 3 and the 1 minute mark was really 2.  It seems that this has , which is a lot more inconvenient than 59 seconds. Apply display settings to all user accounts? Given that$(3x-1)^7=a_7x^7+a_6x^6+a_5x^5+...+a_1x+a_0$, find $a_7+a_6+a_5+a_4+...+a_1+a_0$ Given that$$(3x-1)^7=a_7x^7+a_6x^6+a_5x^5+...+a_1x+a_0$$find $$a_7+a_6+a_5+a_4+...+a_1+a_0$$  Is there anyway to do the question without using binomial theorem and expanding the expression on the LHS?? CSS3 selector to find the 2nd div of the same class I need a CSS selector that can find the 2nd div of 2 that has the same class. I've looked at nth-child() but it's not what I want since I can't see a way to further clarify what class I want. These 2 divs will be siblings in the document if that helps.  My HTML looks something like this:  &lt;div class="foo"&gt;...&lt;/div&gt; &lt;div class="bar"&gt;...&lt;/div&gt; &lt;div class="baz"&gt;...&lt;/div&gt; &lt;div class="bar"&gt;...&lt;/div&gt;   And I want the 2nd div.bar (or the last div.bar would work too). Should Stack Exchange introduce the ability to upload embedded sounds (maybe via HTML5/Flash, whichever the user has) as part of questions and answers to Stack Exchange?  It could require a certain amount of rep to stop new users from doing it frivolously.  My rationale behind this is the new language &amp; usage sites.  I often find myself thinking that it might be helpful, when discussing a regional dialect or something, for the person answering to just pronounce what they're trying to describe in words. How can I effectively use the Coppersmith? I've been playing Dominion with the base + Intrigue sets for a while now, and one of the cards that I have trouble wrapping my mind around is the Coppersmith.  In theory, it seems like a great card - it allows you to make all of your Coppers into Silvers, and in some cases - even Gold. However, I have yet to build a deck during a game that manages to use it effectively. Usually, in order to pull one or two of those with a nice amount of coppers, I need to create a deck that relies heavily on +cards/+actions chains, and the Coppersmith only begins to affect the game too late for it to be of any use.  So... how can this card be effectively used? Are there other schools for witches and wizards in the rest of the world? In the books they only speak of 3 schools, but what about Asian or American people?  And even more, were they affected by the events happening in Europe? Should I say "She is in the park" or "She is at the park"? Show that $x^2+x+4$ is irreducible over $\mathbb Z_{11}$.    The problem can be solved by putting every element from $\mathbb{Z}_{11}$ and checking if there is any root.  $0^2 + 0 + 4 = 4 \\ 1^2 + 1 + 4 = 6 \\ 2^2 + 2 + 4 = 10 \\ 3^2 + 3 + 4 = 5 \\ 4^2 + 4 + 4 = 2 \\ 5^2 + 5 + 4 = 1 \\ 6^2 + 6 + 4 = 2 \\ 7^2 + 7 + 4 = 5 \\ 8^2 + 8 + 4 = 10 \\ 9^2 + 9 + 4 = 6 \\ 10^2 + 10 + 4 = 4 $   But this process is very long one. I am seeking a short method by which I can solve such problem.   Now suppose that it is reducible, then the factors should be linear. So how can we solve the problem based on this kind of observation? Any help will be great. Thanks. Showing that $A\cap B = A\setminus (A\setminus B)$ How does one show that $A\cap B = A\setminus (A\setminus B)$?  My thinking is that if $x\in A\setminus (A\setminus B)$ then this means that $x\in A$ and $x\notin A\setminus B$, which means that $x\in A$ and ($x\notin A$ and $x\in B$), but I don't see why the expression in parentheses should simplify to just $x\in B$. Any insight would be helpful.  Maybe $(x\in A^c$ and $x\in B)$, i.e, $x\in A^c\cap B$ is a possible simplification of the expression in parentheses, but still don't see why this simplifies to just $x\in B$.