How to evaluate cos(2$\pi$/5)? I understand evaluation for cos($\pi$/8), but I cannot figure it out how to solve cos(2$\pi$/5).  Can anyone please show it?
How to prove $\cos \frac{2\pi }{5}=\frac{-1+\sqrt{5}}{4}$? I would like to find the apothem of a regular pentagon. It follows from   $$\cos \dfrac{2\pi }{5}=\dfrac{-1+\sqrt{5}}{4}.$$  But how can this be proved (geometrically or trigonometrically)?
Does the pilot of a rocket ship experience an asymptotic approach to the speed of light? How should I structure my URLs for both SEO and localization? Should I install programs from a source tarball (`.tar.gz`), from the Ubuntu Software Centre, or from elsewhere? How to specify an arbitrary (possibly non-integer) font size in LaTeX I may be wrong, but it seems to me that I cannot obtain non-integer (or non-preloaded) font sizes (say, 9.876pt) using \fontsize.  If this is true, how do I do this in LaTeX?  Do I have to resort to the \font ... at ... primitive?  (The reason I need this is that I'd like to implement a more LaTeXy way to do the \diminuendo macro from .) Creating unnumbered chapters/sections (plus adding them to the ToC and/or header) What does the helpful flag mean? I don't see "Helpful" in the list of things I can do when I press the flag link.   In my profile page I saw "6 helpful flags."  How do I earn these flags?  May I make them on other peoples' posts or comments?   This is what I am talking about: How can I define a custom listing environment? I am trying to define an enviroment for a specific programming language, F#. Here's my code:  \definecolor{bluekeywords}{rgb}{0.13,0.13,1} \definecolor{greencomments}{rgb}{0,0.5,0} \definecolor{turqusnumbers}{rgb}{0.17,0.57,0.69} \definecolor{redstrings}{rgb}{0.5,0,0}  \lstdefinelanguage{FSharp}     {morekeywords={let, new, match, with, rec, open, module, namespace, type, of, member, and, for, in, do, begin, end, fun, function, try, mutable, if, then, else},     keywordstyle=\color{bluekeywords},     sensitive=false,     morecomment=[l][\color{greencomments}]{///},     morecomment=[l][\color{greencomments}]{//},     morecomment=[s][\color{greencomments}]{{(*}{*)}},     morestring=[b]",     stringstyle=\color{redstrings}     }  \newenvironment{fslisting}   {     \lstset{         language=FSharp,         basicstyle=\ttfamily,         breaklines=true,         columns=fullflexible}     \begin{lstlisting}   }   {     \end{lstlisting}   }   Then I'm trying to use it as such:  \begin{fslisting} type 'a Process = 'a Signal IObservable \end{fslisting}   But it doesn't work. The output log says that the listing is not terminated - or is terminated by the document. So the rest of the document is also formatted as a listing, which is of course not the intention.  What am I doing wrong here? Arithmetic progression topology Let $$S=\sum_{n=1}^{\infty}x^{n^2}, \quad|x|&lt;1.$$  It is convergent and the sum is definitely less than $1/(1-x).$   Is there any closed form for $S$ ? PHP 5.5.13 on CentOS 6.5 with yum How can I find maximum power transfer using Thevenin equivalent Why are all known distributions unimodal? Zero visitors? What happened to site analytics about a week ago? I just installed a new version of Ubuntu and I want to roll it back to the previous version.  How can I do that? Is that even possible? When trying to install CrossOver deb I get "Error: Dependency is not satisfiable libpng12-0" Is there a way to get trig functions without a calculator? In school, we just started learning about trigonometry, and I was wondering: is there a way to find the sine, cosine, tangent, cosecant, secant, and cotangent of a single angle without using a calculator?  Sometimes I don't feel right when I can't do things out myself and let a machine do it when I can't.  Or, if you could redirect me to a place that explains how to do it, please do so.  My dad said there isn't, but I just had to make sure.  Thanks. I have the Nikon kit lens that came with a D5100 — the kit lens is  . I was thinking of getting a fast lens and I am looking to buy the .  Should I consider 35mm or instead buy a 55-200mm for better range? Query Feature and Usage based entitlements license I need to query programmatically the Feature license and usage-based license which is available in UI. Could someone please highlight if we can query the same or is it available in UI only, Thanks. Importing a Single Symbol From a Different Font Is there a general way to change the font of a particular symbol without switching packages?  For example, suppose I'm using Computer Modern for my entire document, but I want the "subset" operator to look as it does in mathabx.  How can I redefine it to appear in this way? iPhone SDK: what is the difference between loadView and viewDidLoad? When working with views and view controllers in an iPhone app, can anyone explain the difference between loadView and viewDidLoad?    My personal context, is that I build all my views from code, I do not and will not use Interface Builder, should that make any difference.  I've found that often when I add init code to loadView, I end up with an infinite stack trace, so I typically do all my child-view building in viewDidLoad...but it's really unclear to me when each gets executed, and what is the more appropriate place to put init code.  What would be perfect, is a simple diagram of the initialization calls.  Thanks!