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A detailed tutorial on finding the length of a vector. Step by step tutorial including several examples of how to find the length of a vector for reference.

The length of a vector is also known as the magnitude of a vector. This can be compared to the absolute value of a real number. In order to find the length of a vector, you need to use the Euclidean norm:

The Euclidean norm is a consequence of the Pythagorean theorem.

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A detailed tutorial on seven different basic graphs. Step by step tutorial including several visual examples of seven different basic graphs for reference.

A lot of time in any math class is devoted to the subject of graphs and graphing. But forming a graph when you are only given an equation can be difficult – unless you have some basic graphs memorized. Once you have these seven graphs memorized, it is very easy to follow the patterns in the equation and and simply fix your basic graphs to fit these new requirements. The basic graphs are the most basic patterns that x can be found in on any function – this is x, x squared, and x cubed. There is also the absolute value of x, the  natural log of x, and the exponential function of x. The last one is one divided by x, which while not being a basic form of x, is a very important form.

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A detailed tutorial on identifying coterminal angles. Step by step tutorial including several examples of how to identify coterminal angles for reference.

Coterminal angles are opposite angles that when put together share a terminal side, or common side, and therefore create a circle. One of the angles is positive, and the other angle is negative – a negative angle is one that is formed from the opposite side and using the second scale on a protractor. The absolute value of the first angle plus the absolute value of the second angle must add up to 360 degrees in order for them to be coterminal angles.

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A detailed tutorial on the use of the Absolute Value. Step by step tutorial including a few samples on Absolute Value. Knowledge of the Absolute Value is a requirement for grade school algebra.

Overview

The absolute value of a real number is its numerical value without regard to its sign – it is the distance the number is away from 0. So, for example, 3 is the absolute value of both 3 and −3.

The absolute value of a number a is denoted by | a | .

You can think of the absolute value meaning that the number is positive when you solve equations with it; however, sometimes it is necessary to remember that there’s a possibility the actual number could be negative.

Generalizations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts.