If $0\leq\theta\leq360$, and: $$\tan \theta=2+\sqrt{3}$$  Where $\theta$ is in degrees . How to find $\theta$  (without using a calculator) ? Can anyone give me some hints?
My (very simple) question to a friend was how do I prove the following using basic trig principles:  $\tan75^\circ = 2 + \sqrt{3}$  He gave this proof (via a text message!)  $1. \tan75^\circ$   $2. = \tan(60^\circ + (30/2)^\circ)$  $3. = (\tan60^\circ + \tan(30/2)^\circ) / (1 - \tan60^\circ \tan(30/2)^\circ) $  $4. \tan (30/2)^\circ = \dfrac{(1 - \cos30^\circ)}{ \sin30^\circ}$    Can this be explained more succinctly as I'm new to trigonometry and a little lost after (2.) ?    EDIT  Using the answers given I'm almost there:   $\tan75^\circ$    $\tan(45^\circ + 30^\circ)$   $\sin(45^\circ + 30^\circ) / \cos(45^\circ + 30^\circ)$   $(\sin30^\circ.\cos45^\circ + \sin45^\circ.\cos30^\circ) / (\cos30^\circ.\cos45^\circ - \sin45^\circ.\sin30^\circ)$    $\dfrac{(1/2\sqrt{2}) + (3/2\sqrt{2})}{(3/2\sqrt{2}) - (1/2\sqrt{2})}$   $\dfrac{(1 + \sqrt{3})}{(\sqrt{3}) - 1}$   multiply throughout by $(\sqrt{3}) + 1)$   Another alternative approach:   $\tan75^\circ$    $\tan(45^\circ + 30^\circ)$   $\dfrac{\tan45^\circ + \tan30^\circ}{1-\tan45^\circ.\tan30^\circ}$   $\dfrac{1 + 1/\sqrt{3}}{1-1/\sqrt{3}}$   at point 6 in above alternative
how implement the jqueryUI in visualforce What is the command to remove all files but not directories? Let's say I have a directory tree like this:  FOLDER:     file1     file2     file3     Subfolder1:         file1         file2     Subfolder2:         file1         file2   If I used rm -r FOLDER/*, everything in FOLDER would be deleted including sub-directories. How can I delete all files in FOLDER and in its sub-directories without deleting actual directories? As of now, my desktop has begun showing the contents of my home folder (~) instead of the contents of ~/desktop. I must have changed something, but I have no idea what, or what I was doing exactly when it happened.  How do I re-point gnome to the right folder?  I'm running Ubuntu 11.04. made me think about the movie versions of the 7th book.  In Deathly Hallows Part II      Voldemort has Nagini attack Snape because Voldy thinks that Snape has the Elder Wand's allegiance. We know that Snape didn't actually have the allegiance, Draco did (and by then Harry did) and his plan had failed.   But if Voldy's plan had succeeded with Snape, would he have gotten allegiance?      Since voldemort didn't kill Snape, Nagini did... Basic Web Development IDE/Editor like Dreamweaver? I've used Windows for many years, using Dreamweaver as my editor as it had a file tree which is based on a project (via Local, FTP or SFTP).  I need a web development IDE with the following functionality:   syntax highlighting for PHP, HTML, CSS, JavaScript  file tree - Local, FTP, SFTP, Project-Based (e.g. via the methods of Local/FTP/SFTP) in other words, like Dreamweaver can open multiple files (tabbed)   Additionally, I wouldn't mind features like debugging, class listings, etc, as long as I can hide them away. Why General Leibniz rule and Newton's Binomial are so similar? The binomial expansion:  $$(x+y)^{n} = \sum_{k=0}^{n} \binom{n}{k} x^k y^{n-k}$$  The General Leibniz rule (used as a generalization of the product rule for derivatives):  $$(fg)^{(n)} = \sum_{k=0}^{n} \binom{n}{k} f^{(k)} g^{(n-k)}$$  Both formulas can be obtained simply by induction; Newton's binomial also has a combinatorial proof . It's striking how these formulas are similar; is there a possible connection between them? I was thinking that maybe the General Leibniz rule could be obtained using a combinatorial argument as well (hence the binomial coefficients)... Can I be automatically notified of prolonged blocking in SQL server? About once a week I have to resolve a blocking chain on a SQL Server 2005 database, caused by a long-lived read lock from an Access 2003 front-end. The lock is taken out whenever a user opens a certain form and is released once the user has finished scrolling through the form or closes it. Since many of our users open this form as reference, these locks stay around for a while. Any update to the table causes the blocking, and suddenly nobody can select from this table since they're all waiting on the first lock. This is quite a problem for us, since lots of apps rely on this data. I understand that this locking behavior is part of how Access works with linked tables.  I've been solving the problem from Activity Monitor,  whenever I find out about it. This is a problem not only because it takes me time to do it manually, but also because it's reactive. By the time I hear about it, it's already been a problem for a lot of people.  I'd like to know if there is an automatic way to check for these long-lasting blocking chains, and either be emailed or have the problem resolved automatically. The logic seems straightforward enough ("if any process matching this SELECT query has been blocking for longer than a minute, notify me/kill it") but I don't know how to implement this with SQL Server.  For what it's worth, I think the proper solution is to fix or rewrite the app. However, due to departmental politics, this is not an option for the next few months, so I'm looking for a stopgap. No notification (+15) for accepted answer When should I use exposure compensation? When should I use exposure compensation, rather than ISO, shutter speed or aperture? I'm a newbie to data science, and I do not understand the difference between the fit and fit_transform methods in scikit-learn. Can anybody explain simply why we might need to transform data? What does it mean, fitting a model on training data and transforming to test data? Does it mean, for example, converting categorical variables into numbers in training and transforming the new feature set onto test data? Install button in the software center is grayed out when trying to install .debs without an internet connection I just installed ubuntu 11.10 from a usb stick.   After installation, none of the software which I had collected and run on 11.10 or 11.04 runs on it. Even my newly downloaded opera or chrome installations does not work.  I do not have a internet connection.  Whenever i try to install any .deb file by double clicking it,software center opens up but the install button is grayed out. Suppose I have some theorem in the paper  Section 1 Theorem 1.1. Let ...  And then later in the paper I want to recall the theorem by reprinting it  Section 4 We recall Theorem 1.1: Theorem 1.1. Let ...  What's the proper way to do this? Is there a way to force Google Chrome to remember passwords for sites that have autocomplete turned off? Clarification: I am a programmer, but ideally, I'd like a method that I could help regular users implement, too. : So how many named special cases of each modal verb are there, in toto? There's   1. subjunctive should, and   2. mandative should, and   3. , at least;   and I s[up]pose 4. Should we? is suggestive should, and   5. Shouldn't we? is tag **should**, and I can think of a lot more.    I ask about only operative uses of this modal verb including literary and formal usage,  but please omit anything obsolete. I'm trying to classify them and learn the formal terms describing each. Are there any apt others in addition to the ones above? (I added the enumeration below)  1. What's 'subjunctive should'?  Whenever should is conjugated in the subjunctive mood? 5. What's a tag **should** ? 6. Where does  should/would  feature? What's it called? This should is detailed in   or  or . Reapplying for a UK Standard Visitor visa after a refusal Identifying a short story about time travel and paradoxes I submitted a manuscript last year to an IEEE journal, and the paper was accepted for publication. I recently submitted a new manuscript to the same journal, but, this time, the paper was rejected, and I was told that I should submit to another journal since my paper was not within the journal's scope. The two papers both target similar applications. Furthermore, the second paper uses some work in the first paper, making substantial improvements at solving a much more difficult problem. Based on the reviewer's comments (and my own personal assessment), I do not believe that the work presented in the second paper was "incremental" in nature. Far from it. Two of the three reviewers gave positive reviews. The third reviewer, however, mentioned the "outside of journal's scope" issue and the associate editor and editor-in-chief both sided with the 3rd reviewer, and the paper was stopped dead in its tracks.  I'm scratching my head trying to come to terms with how in the world my first paper could be accepted by this journal, but the second paper focused on the same application space and achieving substantial improvements on a much more difficult problem (backed up with measured results) could be rejected. Any ideas? Vertical uniform circular motion.. can it really be uniform? This is the picture in my mind:    For centripetal force, I learned that: $T-mg\cos\theta= \frac{mv^2}{r}$  In vertical circular motion, the velocity is naturally going to decrease as kinetic energy is converted to potential energy as the particle moves up the circle- and thus resulting into a non-uniform circular motion.  However, I was told that if tension changes accordingly, the velocity will remain constant(as from the equation). What I do not get about this part of the explanation is that which force will balance mgsinθ (tangential force in the diagram  )? Indent entire section using only preamble I heavily use org-mode in Emacs to create TODO lists with timekeeping, which has a handy export to LaTeX feature. The problem is that in order to get my exported LaTeX document to look right, I want to indent entire sections, essentially treating sections like lists. It's very easy to create a template to copy and paste into every new file, but not feasible to edit the text directly as this would interfere with org-modes ease of use. Thus:  Is there a way to indent an entire section, using only the preamble?  MWE  \documentclass{article} \usepackage[explicit]{titlesec} \setcounter{secnumdepth}{0} \newcommand{\clock}{CLOCK: number number number \\}  \titleformat{\section}{\bfseries{}}{\roman{section}}{3pt}{#1} \titlespacing*{\section}{0pt}{0pt}{0pt} \titleformat{\subsection}{\bfseries{}}{\roman{subsection}}{3pt}{$\rightarrow$#1} \titlespacing*{\subsection}{2em}{0pt}{0pt} \begin{document}   \section{First section} \clock  \section{Second section} \clock \clock \clock  \subsection{First subsection} \clock \clock  \subsection{Second subsection} \clock  \subsection{Third subsection} \clock  \end{document}   I want the text with the red arrow to be indented to the same level as the section. How do I clear the render border? In the 3d viewport I am using a border region to only render things inside the selected region. I did this with CtrlB. I cannot get rid of the region. How can I make the border disappear?