## Understanding Supplementary and Complementary Angles

Supplementary and complementary angles are useful concepts to understand in trigonometry. Supplementary angles are any two angles that sum (add) up to 180° (a straight line). An easy way to remember this is that Supplementary and Straight line both begin with the letter ‘S’. Complementary angles are any two angles that sum (add) up to 90° (a corner). An easy way to remember this is that Complementary and Corner both begin with the letter ‘C’. In the above image, we see that angles a and b sum up to 90°, therefore they are complementary angles. In the above image, we see that angles c and d sum up to 180°, therefore they are supplementary angles. While the angles were drawn adjacent to one another, they don’t have to be – although, that is the most common way … Read entire article »

Filed under: Mathematics

## Understanding the differences between various Linux distro’s

There are many different operating systems (OS) out there. The most commonly known being Microsoft Windows and Mac OS, and then there is that OS called Linux that people keep talking about. It is not always clear what Linux is except that its operating system (sometimes claimed to be better than any other operating system on the planet). When you look it up, you are faced with a bewildering choice of operating systems that all claim to be Linux: Red Hat, Ubuntu, Slackware, Mandrake, Linux mint, PC Linux OS, Pear Linux, OpenSUSE, etc. Summary Fundamentally, all Linux distros are very similar. They are based on the Linux kernel which forms the core of all distros. The difference between distros fundamentally boils down to: ease of installation which GUI (Graphical User Interface) they provide (changeable … Read entire article »

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## Understanding the Law of Sines

While trigonometry is used to solve problems involving right angle triangles, it can also be applied to triangles that are not right angle triangles. Assumes you understand basic trigonometric concepts. A tutorial on understanding sine, cosine and tangent can be found here. A tutorial on understanding the trigonometric functions and the unit circle can be found here. What is the Law of Sines One of the fundamental properties of two triangles that have the same shape (i.e., they have the same angles) is that the ratio of any two sides is identical – regardless of the size of the triangles. a A a A b B — = — and — … Read entire article »

Filed under: Mathematics

## Understanding Basic Trigonometric Identities

This tutorial assumes you are familiar with the trigonometric functions and their derivation from the unit circle. A tutorial on the trigonometric functions can be found here. A tutorial on the trigonometric functions and the unit circle can be found here. What is an Identity? An identity (in mathematics) is something that is true (more precisely: a tautological relationship). For example, the following is an identity: 1 + 1 = 2 It says that 1 + 1 is exactly the same as 2. A common (and important) trigonometric identity is: sin2θ + cos2θ = 1 All this identity says is that what is on the left hand side is identical to what is on the right hand side. Why Learn / Use Identities? Identities (in any branch of mathematics) help us to: solve simplify or gain insight into mathematical problems. Identities are a lot like synonyms in … Read entire article »

Filed under: Mathematics

## Understanding Trigonometric Functions using the Unit Circle (Advanced)

While I call this advanced, it does not mean harder or more complicated, it just means more abstract. Understanding the trigonometric functions (sine, cosine, tangent) using right angle triangles is simply a special case of trigonometric functions using the unit circle. I strongly recommend first reading and understanding the article Understanding Sine, Cosine, and Tangent first, because it explains the history and reasoning behind the trigonometric functions. This is the way trigonometric functions are generally understood and defined in mathematics. Trigonometric functions were originally developed and understood from the study of right angle triangles. The problem with using right angle triangles is that trigonometric functions can only be defined for angles between 0° and 90°, but not for angles ≤ 0° or ≥90° because no such right angle triangles exist. The Unit Circle The Unit … Read entire article »

Filed under: Mathematics

## Understanding Sine, Cosine and Tangent

An article explaining trigonometric functions using the unit circle can be found here Using the unit circle is the standard way trigonometric functions are defined and understood in mathematics. I recommend reading and understanding this article first. Later, if you want to understand how trigonometric functions are defined for values greater than 90° or less than 0°, go and read the other article. Sine is often introduced as follows: Which is accurate, but causes most people’s eyes to glaze over. The problem is that from the time humans starting studying triangles until the time humans developed the concept of trigonometric functions (sine, cosine, tangent, secant, cosecant and cotangent) was over 3000 years. A Little History The ancients studied triangles. One of the things they did was to compare the lengths of the sides of triangles: A triangle has … Read entire article »

Filed under: Mathematics

## Ubuntu 12.04 – Basic Unity Interface / Desktop Tutorial

This is a basic tutorial for the Unity Interface / Desktop which comes with Ubuntu 12.04 – it should help get you up and running. There are differences between Unity shipped with Ubuntu 11.10 and Ubuntu 12.04. This tutorial reflects the way I understand and use the Unity interface. The Unity interface consists of four main parts: Panel Launcher Dash HUD The Panel The Panel is the strip at the top of the interface: The menu bar that you are used to seeing near the top of an application’s window is now displayed in the panel: There is a catch: The menus displayed in the Panel are only for the active (topmost) application window. The menus are only displayed when you hover your mouse over the Panel, otherwise, the Panel is empty. If a window is maximized (full screen), the buttons (icons) for minimize, … Read entire article »

Filed under: Ubuntu 12.04

## Understanding Averages – Mean, Median, and Mode

This tutorial examines the concept of the average as a single value representing a collection of values. It focusses on the mean, median, and mode. The average (especially in physics) can also mean the center or balance point, but, for most everyday use, we tend to think of the average as representative value. Average comes from the Old French avarie which came from the Old Italian avaria which came from the Arabic awariyah meaning damaged goods or merchandise. Which is probably apt, given how how badly averages are often misused. The Old French avarie used to mean the damage sustained to a ship or its cargo. The meaning later shifted to mean an equal distribution of the costs of such damage. For example, if ten men pooled money together and hired a ship … Read entire article »

Filed under: Mathematics

## Keyword – switch, case, default

The switch keyword is probably the least well understood of the C/C++ language keywords (although, const probably comes a close second). The keywords switch, case, and default always go together and cannot be used independently in any other context. There is a small difference in behaviour between C and C++. Most programmers will never notice the difference. The most common use of switch is as a replacement for multiple if-else statements: switch (value) … Read entire article »

Filed under: C, C++

## Ubuntu 11.10 – Understanding sudo apt-get install …

This tutorial is for Ubuntu 11.10, however, it should be the same for other versions of Ubuntu (and derivatives, like edubuntu, kubuntu, lubuntu, and xubuntu) and other Linux distributions based on Debian. However, no guarantee is made. What makes Ubuntu very easy to use is the Ubuntu Software Center which allows users an easy way to select and install or remove packages (usually programs). However, when you search the web looking for help with Ubuntu, often times you see something to the effect of: Enter the following command: sudo apt-get install lubuntu-desktop While this is clear for those who know what it means, I believe the majority of Ubuntu users are those who want a simple to install and use Linux OS – they are not interested in lower level details of managing their system. In … Read entire article »

Filed under: Ubuntu, Ubuntu 11.10