User:Thatha

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This page is under heavy construction! For the time being visit my blog.

Languages, Scripts, and Grammar

G	This user is a student or alumnus of Grinnell College.

en	This user is a native speaker of English.

el	Αυτός ο χρήστης έχει ως μητρική γλώσσα την ελληνική.

grc-3

Ὅδε ὁ ἐγκυκλοπαιδειουργὸς τὴν ἀρχαίαν Ἑλληνικὴν γλῶτταν γράφειν ἀνωτέρως οἷός τ’ ἐστιν.

de-2

Dieser Benutzer hat fortgeschrittene Deutschkenntnisse.

fr-1

Cet utilisateur peut contribuer avec un niveau élémentaire de français.

ja-1

この利用者は少しだけ日本語を話すことができます。

ipa-3

This user has an advanced understanding of the International Phonetic Alphabet.

~~mankind~~

This user supports the use of gender-neutral language.

they

This user considers singular they standard English usage.

snkt

This user says sneaked.

infin¦
itive

This user chooses never to split infinitives.

by	The passive voice may be used by this user.

…in.

Ending a sentence with a preposition is something this user is okay with.

whom

This user insists upon using whom wherever it is called for, and fixes the errors of whomever he sees.

which & that

This user knows how to use which and that correctly.

!?	This user is a punctuation stickler.

. The

This user does not put two spaces after a full stop.

,	This user fixes comma splices as they are annoying.

A, B, and C

This user prefers the serial comma.

Mix

This user has been influenced by too many dialects of English to use one orthography, vocabulary and grammar consistently.

About Me

18	This user is 18 years old.

This user comes from Greece.

Computing

AIM-Able

This user understands AIM talk perfectly well, but does not use it. Ever.

c-2

This user is an intermediate C programmer.

asp

This user can code in ASP.

asm

This user can program in assembly language.

C++

This user can program in C++.

java

This user can program in Java.

pas

This user can program in Pascal.

php

This user can program in PHP.

This user can program in Scheme.

ruby

This user is a Rubyist.

bash

This user is a bash scripter.

<html>

This user can write HTML.

js	This user can program in JavaScript.

This user can code in L^AT_EX.

mysql

This user writes programs that access MySQL.

re	This user is a regular expression programmer.

xhtml

This user can write XHTML.

prog-4

This user is an expert programmer.

@	This user can be reached by email.

This user's AOL Instant Messenger screenname is thatha7777.

This user uses Jabber as thatha@jabber.org.

	This user uses Skype. Contact this user

YIM

This user's Yahoo! Messenger screename is thatha7777.

This user has a website, which can be found here.

dA	This user is a deviantART deviant at thatha

digg

This user is a contributor to Digg.

f	This user maintains a facebook profile.

last
.fm

This user tracks what they listen to on Last.fm.

This user maintains a blog.

W	This user uses WordPress.

G	This user uses Google as a primary search engine.

OWN

This user uses an email account with their own domain name.

This user uses Adium to chat on various instant messaging networks.

This user contributes using The GIMP.

This user prefers Mozilla Firefox.

This user contributes using Safari.

This user runs Mac OS X.

g	This user contributes using Gentoo Linux.

This user contributes with Red Hat Linux.

This user contributes using Debian.

This user contributes with GNOME.

This user contributes using Microsoft Windows.

This user contributes using Nano.

This user contributes using Vim.

This user writes with the OpenOffice.org suite.

This user contributes using a PDA.

This user contributes using a laptop.

DUO

This user contributes with a computer based on the Intel Core Duo microprocessor.

This user contributes using an Apple Mac mini computer.

This user contributes using a wireless connection.

>56k

This user is contributing using a broadband connection.

Preferences

This user is a carnivore.

This user believes that Caffeine is necessary in large doses daily.

This user drinks hot chocolate.

This user drinks orange juice.

Template:User H20

This user drinks tea.

This user believes that you should never put milk in with the tea bag.

Piña

This user likes the sweet flavour of the Piña Coladas.

C₂H₆O-2

This user drinks occasionally.

cvg-0

This user does not play/is not interested in computer and video games.

This user plays games on a graphing calculator.

This user is interested in ancient civilizations.

This user is interested in the ancient Celts.

This user is interested in ancient Greece.

$\sum_{i=1}^{\infty}{1 \over i^2}$

This user is an advanced mathematician.

λ	This user is fluent in Lambda calculus.

This user uses the metric system and loves it.

Pi = 3.141592653589793238462643383 27950288419716939937510582097494 45923078164062862089986280348253 42117067982148086513282306647093 84460955058223172535940812848111 74502841027019385211055596446229 48954930381964428810975665933446 12847564823378678316527120190914 56485669234603861045432664821339 36072602491412737245870066063155 88174881520920962829254091715364 36789259036001133053054882046652 1384146951941511609 . . .

flute

This user plays the flute.

This user plays the piano.

This user plays the recorder.

This user listens to World Music

This user enjoys classical music.

This user enjoys pop music.

This user enjoys rock music.

This user enjoys
metal music.

This user enjoys indie rock.

This user is an audiophile.

iTS	This user uses the iTunes Store.

Cass

This user knows that you gotta make your own kind of music.

This user is interested in Linguistics.

This user misses Pluto. May its planethood rest in peace.

This user loves calculators.

This user enjoys electronics or is an electronics hobbyist.

'	This user has the knack.

This user prefers cold weather.

This user enjoys pistol shooting.

This user is a bicyclist.

This user couldn't care less about football.

This user is a bibliophile.

This user is interested in Criminology

This user does not like socklessness.

This user is interested in law.

This user is an art lover.

This user enjoys cooking.

This user enjoys photography.

This user enjoys writing.

This user is a cats lover.

This user's home is overrun with cats.

This user is a member of the worldwide family of Scouts.

[edit] Calculating $\int \csc{x} \;dx$

$\int \csc x \;dx$ = $\int \frac{1}{sin{x}} \;dx$ = $\int \frac{1}{2 \sin{\frac{x}{2}} \cos{\frac{x}{2}}} \;dx$ = $\frac{1}{2} \int \frac{1}{ \sin{\frac{x}{2}} \cos{\frac{x}{2}}} \;dx$ , since $\sin{\theta}=2 sin{\frac{\theta}{2}} cos{\frac{\theta}{2}}$ (Double-angle formulae).

$\frac{d}{dx} \ln{|\tan{x}|}$ = $\frac{1+\tan^2{x}}{\tan{x}}$ = $\frac{\sec^2{x}}{\tan{x}}$ = $\frac{1}{\cos^2{x}\tan{x}}$ = $\frac{1}{\cos^2{x}\frac{\sin{x}}{\cos{x}}}$ = $\frac{1}{\sin{x}\cos{x}}$ , thus $\int \frac{1}{ \sin{x} \cos{x}} + C \;dx$ = $ln | tan x |$ , where $C$ is a constant of integration.

Thus, $\frac{1}{2} \int \frac{1}{ \sin{\frac{x}{2}} \cos{\frac{x}{2}}} \;dx$ = $\frac{1}{2} 2 \ln{|\tan{\frac{x}{2}}|} + C$ = $\ln{|\tan{\frac{x}{2}}|} + C$ .

To summarize, $\int \csc{x} \;dx$ = $\ln{|\tan{\frac{x}{2}}|}$ = $ln | csc x - cot x |$ (because $\tan{\frac{x}{2}} = \csc{x} - \cot{x}$ ).

[edit] Proving that $\tan{\frac{x}{2}} = \csc{x} - \cot{x}$

$\tan{\frac{x}{2}} = \csc{x} - \cot{x}$ can also be written as $tan x = csc2 x - cot2 x$ .

$csc2 x - cot2 x$ = $\frac{1}{\sin{2x}} - \frac{\cos{2x}}{\sin{2x}}$ = $\frac{1-\cos{2x}}{\sin{2x}}$ = $\frac{1-(1-2\sin^2{x})}{2\cos{x}\sin{x}}$ = $\frac{2\sin{x}\sin{x}}{2\cos{x}\sin{x}}$ = $\frac{\sin{x}}{\cos{x}}$ = $tan x$