Please keep in mind that I am only a beginner when it comes to trigonometry. I understand that sine is opposite/hypotenuse, cosine is adjacent/hypotenuse and that tangent is opposite/adjacent. My questions is that when you input sin(B)=AC/Hypotenuse (when hypotenuse and B is given to us). What does the calculator do to get the answer.
Sine $\theta$ = opposite/hypotenuse   Cosine $\theta$  = adjacent/hypotenuse   Tangent $\theta$  = opposite/adjacent      In order to calculate the sine or the cosine or the tangent I need to know $3$ sides of a right triangle. $2$ for each corresponding trigonometric function. How does a calculator calculate the sine, cosine, tangent of a number (that is actually an angle ?) without knowing any sides?
I am currently writing a paper with several multiple regression analyses. While visualizing univariate linear regression is easy via scatter plots, I was wondering whether there is any good way to visualize multiple linear regressions?   I am currently just plotting scatter plots like dependent variable vs. 1st independent variable, then vs. 2nd independent variable, etc. I would really appreciate any suggestions. Strange behaviour of binomial coefficient's delimiters This question led to a new package:      While writing down my Combinatorics exercises I found that the binomial coefficient's delimiters weren't displayed as indicated inside the amsmath documentation.  By subsequent trials and errors I was able to reduce the volume of my document to this simpler and fully compilable MWE:  \documentclass[11pt]{article} % \usepackage{amsmath} % \makeatletter % \usepackage{lmodern} \usepackage{lipsum} % \makeatother % \begin{document} % \lipsum[1] \begin{equation} 2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2} \end{equation} \lipsum[1] % \end{document}   Which gives (using TeXworks 0.44 on MikTeX 2.9.4521 updated 09/10/13) this un-expected result:        While the amsmath doc shows that with the loaded packages inside the MWE the result would actually be like this:        From here we can see that the delimiters on the first example are a little bit stretched vertically as they surpass the arguments inside the binom. coeff.  The more strange event is that when I comment the line \usepackage{lmodern} the result on delimiter's shape in my example looks exactly as the amsmath doc:  \documentclass[11pt]{article} % \usepackage{amsmath} % \makeatletter % %\usepackage{lmodern} \usepackage{lipsum} % \makeatother % \begin{document} % \lipsum[1] \begin{equation} 2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2} \end{equation} \lipsum[1] % \end{document}   Output:        From here I deduce that the problem lies inside lmodern, but I'd like to keep using this package and fix this wierd "issue" with the math mode. Is there some clue that I've missed or this is in fact an update-process bug infecting amsmath's delimiter control? I am looking to prove the following statement false:  Let $k$ be a positive integer, then $k\mid n$ if and only if $k\mid n^2$.  So I am trying to find a $k$ where this does not hold but after aimlessly trying numbers I was curious if there is a methodical way to find $k$. I am working on a prototype, one function of which is to detect whether an object is "in range" by a few cm. Right now I'm just using an Arduino and a cheap  that operates at 13.56 MHz:    I've successfully gotten it to detect the tag, but only at a distance of about 3-4 cm when the tag is oriented parallel to the antenna.  According to my  , the HF band allows read ranges of between 10 cm and 1 m for passive tags, depending on factors like antenna size, tag size and orientation, and transceiver power.  I realize this inexpensive reader is not up to task as-is, but I'm interested in building something that achieves read ranges of 15-20 cm.  Some criteria:   No need to read multiple tags; only whether one tag is in range or not. No need to write to the tag. Cannot use an active tag.   I'm not experienced with RFID reader construction (yet) but am interested in knowing what I should pursue.  Here are some things I've considered:   Ditch the embedded antenna on the cheap RFID reader and construct my own, larger antenna. I'd need to see if the onboard  is up to the task of providing additional power. Look for a different IC around which to build a reader from scratch. Find a ready-made solution instead of trying to build one (more cost-effective?). Use something other than RFID for simple proximity detection.   I am experienced with microcontrollers and basic electronics, and have made audio and lighting projects, but this is a first with RFID. Since I don't need to read multiple tags, which RFID is suitable for, I've considered maybe some sort of magnet and hall-effect sensor, but the range does not seem adequate. I considered using an ultrasonic proximity detector, but the application calls for detecting the tagged object while ignoring untagged ones (ultrasonic would produce false positives on untagged objects). I've considered some sort of reflective surface placed on the object, and detecting reflected light, but the object orientation is not reliable enough to maintain alignment.  So, in a nutshell, What modifications can I make to my existing reader, or what alternate technology should I pursue to achieve 15-20 cm detection of a passively tagged object?  I plan on connecting whatever proximity detector is used to a microcontroller using SPI. Has anyone ever booked a flight with ?  I am just wondering where they get their prices and data from, and if I might find a cheaper flight by using something like Expedia or Travelocity. At least two questions (, ) on this site indicate that in more than a few isolated cases at least, letters of recommendation are in fact written by the applicant and only signed off (or perhaps rephrased somewhat) by the recommender, who would actually be responsible for writing the letter.  Is there any evidence about the prevalence of this practice that goes beyond anecdotes? I realize that cross-country (cultural) difference may play a role. Is there any truth to the idea that you shouldn't multiply seasonings when multiplying a recipe? I often hear cooks discuss that idea that if you are multiplying, say, a recipe for 4 to be a for 32, that you shouldn't multiply some herbs, spices, or salt. I've never understood any reason why this should be true. Maybe something to do with surface area to volume ratios, or cooking times? Does anyone have a real explanation, or is this nonsense? Definite article — “on television” vs. “on the radio” Why are these different?        We heard the news on the radio.   We watched the news on television.      In this , the author says we must use television without the. Why? It makes me crazy. Is there a valid reason? Parallel option performing worse on cluster I'm trying out oracles parallel option on a cluster and surprisingly I am getting worse results with the parallel option. I was expecting some improvement with the parallel option but certainly not worse results. I am wondering why this is the case, and if there is anything wrong with the way I am using the parallel option on my cluster.   I am using a degree of 4 when the number of CPU's I have is 8. I have tried adding parallel to the cluster directly ALTER CLUSTER cluster PARALLEL 4 as well as at the statement on both the index /*+ PARALLEL_INDEX(clust_index, 4) */and tables /*+ PARALLEL(4) */,   Here is my trace from the parallel:    Without parallel: Unsung hero dilemma This is partly related to  question.  I ran some queries on odata for my work on Stack Overflow, and I have found that my statistics are the following ones:  Accepted answers: 148 Zero score accepted answers: 36 Percentage of total: 24,3%  I probably fit the idea of the Unsong hero badge, as I've mostly been active in  questions, from when it only had around 200 Questions until now.  To get the badge I could either try to get one of my accepted answers downvoted once, that would give me a 25% accept rate; I could also delete 4 of my accepted answers with 1 or more score. That would also give me the badge, but this just seems wrong: You are actually encouraging me to either try to get a down-vote on a good answer, or delete good answers.  So, should I delete good answers to receive a gold badge?  Update: It's not that I care much if I get a badge or not, it's only a badge after all and not why I spend time on Stackoverflow anyways. But it's not ideal [read: problem] that I'm encouraged to delete accepted answers or try to get downvotes to achieve a badge. How to delineate watersheds in QGIS? I am using qgis 2.14.17 with ubuntu16. Having as input data a DEM of the region and a river network. In the manual of qgis they suggest to use a toll of qgis: Catchment area (Parallel); I dont have this in my toolbox, anybody made the same experience and could tell me the reason for it and how to get it. It seems to offer the best solution for me.  Tools which are available are from GRASS7 and TauDEM, the latter need much more data it seems. And I am not sure if I am able to create these just out of a DEM? The GRASS7 has one tool r.water.outlet: but here one has to put the outlet coordinates, which clearly I could get out of the river network, but the idea is that they are generated by delineating the watersheds.  Somebody has an idea how to solve it?  I managed now to get SAGA run in the toolbox, nevertheless would be great if somebody could help me with the qgis tool, since it should appear?! Stopping resetting of linked locators in manipulate How do I get the size of a java.sql.ResultSet? Shouldn't this be a pretty straightforward operation? However, I see there's neither a size() nor length() method. Bibliography contents (Journal names) not abbreviated even with IEEEabrv I am using the following syntax, with no errors or warnings. However, the journal names are still not abbreviated. I compiled the file numerous times, as well as the bibliography. Everything compiles with no errors.  The syntax:   \bibliographystyle{IEEEtran} \bibliography{IEEEabrv,references}   Additional info: I am using BibDesk and TeXStudio on a macbook.  Do you have any idea what might be the issue? and how to solve it? Thank you.  Edit:  Example entry from the IEEEabrv file:  @STRING{IEEE\_M\_COM        = "{IEEE} Commun. Mag."}   Example entry from my references file:  @article{dai:2015,     Author = {Test, T.},     Journal = {IEEE\_M\_COM },     Month = {September}     } Change email login to another id My original email id got compromised and now I want my new email id to be the main id for all SE sites . How to delete original id from the system as someone else might login from it ? This is tricky. I would like to install Ubuntu on a machine that is intended to work as server, and for some reason I do not have an option to connect a screen to it.  I expect this may be similar to remote installation. However, there is currently no OS on that machine, so I will have to set up everything from scratch.  On the other hand, I do have a physical access to that machine. Therefore I can get it to boot from a CD/USB. But that's not enough.  Is there a way to do such installation remotely? Is there a version of Ubuntu image that comes with a SSH server preinstalled, and starts it once booted, so that I can boot the machine with such image, connect to it via SSH and process the installation from a different computer?  If not, what other options do I have? (1) Does he not know? (2) Doesn't he know?  I don't usually see and hear questions formed in the first style. I was even surprised to know that it is grammatically correct. And actually it is the most &quot;proper&quot; way to form an interrogative sentence.  shows that the first style was much more popular before than now. What are your suggestions on choosing between these styles? And I will probably add the third one.  (3) He does not know?  EDIT: The answers have explained how to form a question, but have not actually provided an account on the usage of the first two forms. Especially I'm interested in the first form: does it sound formal, is it used in speech or only in writing, et cetera. What is a comprehensive definition of Philosophy? Alternatively, is it impossible to define Philosophy? This is a pseudo- question, but it seems like it belongs here. find all the members of A4/K Let K={(1),(12)(34),(13)(24),(14)(23)} show that K is a normal subgroup of the alternating group of degree A4 and find all the members of A4/K and write down the group table for A4/K.   i know that K is the Klein four group and i have already proven it is a normal subgroup but i need a start on approaching the A4/K part of this question no direct answers are necessary,just ideas thank you! :) I was wondering how to run a command as another user from a script.  I have the script's owner set as root. I also have the following command being run within the script to run the command as the hudson user:  su -c command hudson   Is this the correct syntax?