Posts Tagged ‘side’
Thursday, December 24th, 2009
Finding the Function of a Directed Graph
Description
A detailed tutorial on finding the function of a directed graph. Step by step tutorial including several examples of finding functions of digraphs for reference.
Overview
A directed graph, more commonly known as a digraph, is the visual representation of a function or of a relation. As in any graph, there are points and lines – called vertices and edges in a digraph. Each edge has an arrow pointing to a vertex. The first vertex – the one the arrow comes from – is the x coordinate of an ordered pair. The second vertex – the one the arrow is pointing to – is the y coordinate of an ordered pair. In the case of double-sided arrows, two ordered pairs are made, with the x and y coordinates switching. This is done for every single vertex and edge on the graph.
Tags: arrow, coordinate. ordered, digraph, directed, discrete math, double, edges, expression, First, function, graph, lines, pair, points, relation, representation, second, side, vertex, vertices, visual, x, y
Posted in Discrete Math | No Comments »
Tuesday, November 17th, 2009
How to Find Slant Height
Description
A detailed tutorial on how to find the slant height. Step by step tutorial including several examples of how to find the slant height for reference.
Overview
The slant height is an additional measure of height that is used for the different types of triangular prisms. The common traingular prisms are your typical pyramid, and cones. On a pyramid, the slant height is the height of one of the triangular faces. On a cone, the slant height is to be found using a formula that is only for the cone. It is the square root of the radius squared added to the real height squared.
Tags: 3D, base, cone, face, figure, geometrical, Geometry, height, polyhedron, prism, pyramid, shape, side, slant, triangle, triangular
Posted in Geometry | No Comments »
Friday, November 13th, 2009
Overview of Polyhedrons
Description
A detailed tutorial on polyhedrons. Step by step tutorial including several examples and a visual example of polyhedrons for reference.
Overview
Mathematicians have not yet decided what truely makes something a polyhedron, but in general they are accepted to be some 3D geometrical figure that has sides or faces, and usually at least one base. There are regular polyhedrons, which have all the same polygon making up their faces, and irregular polyhedrons – which are actually more common – where there are 2 or more shapes in them.
Tags: base, common, decagon, face, figure, geometrical, Geometry, hexagon, irregular, pentagon, polygon, polyhedron, regular, shape, side, square, triangle
Posted in Geometry | No Comments »
Tuesday, November 10th, 2009
How to Find the Opposite and Adjacent Sides of a Triangle
Description
A detailed tutorial on how to find the opposite and adjacent sides of a triangle. Step by step tutorial including several examples of finding the opposite and adjacent sides of a triangle for reference.
Overview
When using SOHCAHTOA, you will often see something such as “find the opposite side” or “find the adjacent side.” Unlike the hypotenuse, the opposite and adjacent sides change depending on what angle you are working with. The right angle is found opposite the hypotenuse and you will never be working it. Tip your triangle so that your right angle is balanced across the bottom and left, and your hypotenuse crosses the right. You will be working with the angles on the top and on the bottom right. The adjacent side is one of the sides that forms your angle – one of which is the hypotenuse, so it is the other side. And to find the opposite side, draw a straight line from your angle. The line it crosses should be the one directly across from your angle, and it is the opposite side.
Tags: adjacent, angle, cosine, hypotenuse, opposite, pythagorean theorem, side, sine, SOHCAHTOA, tangent, trig, trigonometry
Posted in Trigonometry | No Comments »
Thursday, October 22nd, 2009
How to Identify the Initial Side
Description
A detailed tutorial on the intial side of an angle. Step by step tutorial including several examples of the initial side of an angle for reference.
Overview
The initial side of an angle is the side of an angle where the measurement begins. An angle is always measured from the degree of zero to the degree of the angle, regardless of if the angle is positive or negative. The best display of an initial side would be when you draw angles with a protractor – the line that you trace along the bottom of your protractor forms a ray which is known as the initial side.
Tags: angle, begins, ends, Geometry, initial, measurement, negative, positive, ray, side, terminal, triangle
Posted in Geometry | No Comments »
Thursday, October 22nd, 2009
How to Identify the Terminal Side
Description
A detailed tutorial on the terminal side of an angle. Step by step tutorial including several examples of the terminal side of an angle for reference.
Overview
The terminal side of an angle is the side of an angle where the measurement ends. An angle is always measured from the degree of zero to the degree of the angle, regardless of if the angle is positive or negative. The best display of a terminal side would be when you draw angles with a protractor – the line that you draw for your degree forms a ray which is known as the terminal side.
Tags: angle, begins, ends, Geometry, initial, measurement, negative, positive, ray, side, terminal, triangle
Posted in Geometry | No Comments »
Friday, October 16th, 2009
How to Identify Coterminal Angles
Description
A detailed tutorial on identifying coterminal angles. Step by step tutorial including several examples of how to identify coterminal angles for reference.
Overview
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.
Tags: 360, absolute value, angle, circle, coterminal, degrees, Geometry, Math, negative, opposite, positive, protractor, side, terminal
Posted in Geometry | No Comments »
Friday, October 9th, 2009
Definition of a Semiperimeter
Description
A detailed tutorial of what a semiperimeter is. Step by step tutorial including a visual example of a semiperimeter for reference.
Overview
In geometry, a semiperimeter of a polygon (squares, rectangles, triangles, or any closed and none-rounded shape) is simply half a perimeter – like a radius would be for a circle, almost. If you already have the perimeter of the figure, you can easily obtain the semiperimeter by dividing it in half. The semiperimeter is given its own seperate variable and identity because it is used sometimes in mathematical equations, such as Heron’s formula.
Tags: divide, Geometry, Heron's Formula, identity, Math, perimeter, polygon, semiperimeter, side, variable
Posted in Geometry | 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 »
Thursday, October 1st, 2009
Introduction to the Parallelogram Law
Description
A detailed tutorial of the parallelogram law. Step by step tutorial including several examples of the parallelogram law for reference.
Overview
The parallelogram law shows up in many forms, but the simplest form states that the sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals. Assuming that a rectangle has four corners A, B, C, and D, this can be expressed as:
Typically, the two diagonals of a parallelogram are not equal in length. If they are, then the equation simplifies to the Pythagorean theorem. A more complicated version of the parallelogram law is often found when calculating vectors.
Tags: diagonals, Geometry, law, length, Math, parallelogram, pythagorean theorem, rule, side, square, sum
Posted in Geometry | No Comments »
