Posts Tagged ‘right’
Thursday, October 22nd, 2009
How to Identify the Phase Shift
Description
A detailed tutorial on the phase shift of a function. Step by step tutorial including several examples of the phase shift of a function for reference.
Overview
The phase shift is another way of saying a horizontal shift – that is, when a graph moves from left to right. If the phase shift is positive, the graph shifts to the left, and if the phase shift is negative, the graph shifts to the right. Finding a phase shift is not difficult – when a value is included with x (instead of included with something relating to x), then a horizontal shift or phase shift will be performed. Simply look at the equation of the function to find the value.
Tags: algebra, equation, function, graph, horizontal, left, negative, phase, positive, right, shift, value, x
Posted in Algebra | No Comments »
Thursday, October 8th, 2009
An Introduction to the Law of Tangents
Description
A detailed tutorial on the Law of Tangents. Step by step tutorial including several examples of the Law of Tangents for reference.
Overview
The Law of Tangents refers to the lengths of the three sides of a triangle and the tangents of the angles. This can be used with respect to any triangle, not just right triangles. While the Law of Tangents is not as well known as the Law of Sines or the Law of Cosines, it is useful. The Law of Tangents can be used whenever either two sides and an angle, or two angles and a side, are known on any given triangle. The proof of this law starts with the Law of Sines. The Law of Tangents is as follows:
![\frac{a-b}{a+b} = \frac{\tan[\frac{1}{2}(\alpha-\beta)]}{\tan[\frac{1}{2}(\alpha+\beta)]}.](http://s.wordpress.com/latex.php?latex=%5Cfrac%7Ba-b%7D%7Ba%2Bb%7D%20%3D%20%5Cfrac%7B%5Ctan%5B%5Cfrac%7B1%7D%7B2%7D%28%5Calpha-%5Cbeta%29%5D%7D%7B%5Ctan%5B%5Cfrac%7B1%7D%7B2%7D%28%5Calpha%2B%5Cbeta%29%5D%7D.&bg=ffffff&fg=000000&s=0 "\frac{a-b}{a+b} = \frac{\tan[\frac{1}{2}(\alpha-\beta)]}{\tan[\frac{1}{2}(\alpha+\beta)]}.")
Tags: angle, ASA, law, law of cosines, law of sines, law of tangents, length, Math, right, side, SSA, tangent, tangents, triangle, trigonometry
Posted in Trigonometry | No Comments »
Tuesday, September 15th, 2009
An Overview of the Different Types of Triangles
Description
A detailed tutorial on the different types of triangles. Step by step tutorial including several examples of the different types of triangles for reference. Knowledge of the different types of triangles is required for all geometry classes.
Overview
Everyone knows what a triangle is, but a triangle is more than just “a triangle” – it could be one of several different types of triangles. Different types of triangles are identified by the different traits of their sides and their angles. The types are as follows:
Scalene Triangles: All sides and all angles are of different measures and lengths.
Right Triangles: One angle of the triangle is 90 degrees.
Isosceles Triangles: 2 sides and 2 angles have the same measures and lengths.
Equilateral Triangles: All side lengths are the same and all angles are 60 degrees.
Equiangular Triangles: All angles measure 60 degrees but all sides could have different lengths.
Tags: 60, 90, angle, degrees, equal, equiangular, equilateral, Geometry, isosceles, length, Math, measure, right, scalene, side, triangle
Posted in Geometry | No Comments »
Tuesday, September 15th, 2009
All About 30-60-90 Triangles
Description
A detailed tutorial on the solving of 30-60-90 triangles. Step by step tutorial including several examples of how to solve 30-60-90 triangles for reference.
Overview
A 30-60-90 triangle is a special type of right triangle. The 30-60-90 refers to the measure of the angles of the triangle. This triangle is special because if you take two of them, flip one of them over, and place the triangles back to back, then you have an equilateral and equiangular triangle – triangles that have sides and angles all of the same length.
Tags: 30, 30-60-90, 60, 90, angles, equal, equiangular, equilateral, Geometry, Math, right, sides, triangles
Posted in Geometry | No Comments »
Tuesday, September 15th, 2009
All About 45-45-90 Triangles
Description
A detailed tutorial on the solving of 45-45-90 triangles. Step by step tutorial including several examples of how to solve 45-45-90 triangles for reference.
Overview
A 45-45-90 triangle is one of the few special triangles that the angles are always the same on – the 45-45-90 part refers to the measurement of the angles. A 45-45-90 triangle is special because it is the only right triangle where the other two angles are equal. Because the angles are equal, this also means that those sides are of equal lengths.
Tags: 45, 45-45-90, 90, angles, equal, Geometry, Math, right, sides, triangles
Posted in Geometry | No Comments »
Friday, September 11th, 2009
How to Translate Graphs
Description
A detailed tutorial on the translation of graphs. Step by step tutorial including several examples of translating graphs for reference.
Overview
There are different ways to translate graphs, but the easiest way is to memorize the general rules for translation. This tells you what parts of the equation do what to your basic graph. Starting with a graph of y = f(x), these would be your basic rules:
y = f(x – a) moves a units to the right
y = f(x + a) moves a units to the left
y = f(x) + a moves a units up
y = f(x) – a moves a units down
y = f(-x) reflects over the y-axis
y = -f(x) reflects over the x-axis
Reflections are always done before translations, not the other way around, because if you do your translation first you will end up with your shape having the wrong coordinates.
Tags: algebra, down, graph, graphing, graphing techniques, graphs, left, Math, refliection, right, translate, translation, up
Posted in Algebra | No Comments »
Thursday, September 3rd, 2009
An Introduction to Basic Angles
Description
This video explains the various type of angles and why each angle is classified in certain categories. Examples of uses in math and uses in the real world are provided in the video and the picture examples are organized into the different categories for angles.
Overview
Angles are points that are measured in the unit degrees. They are used often in mathematics and are seen in the shape of a triangle. There are several different types of angles. The most common ones are acute angles, right angles, and obtuse angles. The way to remember these is an acute angle = a cute angle. Small things are considered cute and small angles are acute angles. Right angles = correct angles. Something that is perfectly straight and squared off is considered to be correct, like a right angle. Once you remember these, obtuse must be the remaining angle.
Acute Angles: Angles measuring less than 90 degrees
Right Angles: Angles measuring 90 degrees
Obtuse Angles: Angles measuring more than 90 degrees
Protractors are used to measure degrees if you are curious as to whether or not your angle is acute, right, or obtuse.
Tags: acute, angles, degrees, Geometry, Math, obtuse, protractor, right, triangles
Posted in Geometry | No Comments »
