Posts Tagged ‘angle’
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 »
Tuesday, November 10th, 2009
Identifying Convex Polygons
Description
A detailed tutorial on identifying convex polygons. Step by step tutorial including several examples of how to identify convex polygons for reference.
Overview
Convex polygons are polygons that seem to curve inwards. They may appear rather big compared to concave polygons. The best way to identify a convex polygon is to check for a reflex angle. A reflex angle looks like an obtuse angle, or an arrow cutting into the figure. Concave polygons have reflex angles, convex polygons don’t. All regular polygons are considered convex polygons.
Tags: angle, big, convex, curve, Geometry, obtuse, out, polygon, reflex, regular
Posted in Geometry | No Comments »
Tuesday, November 10th, 2009
Identifying Concave Polygons
Description
A detailed tutorial on identifying concave polygons. Step by step tutorial including several examples of how to identify concave polygons for reference.
Overview
Concave polygons are polygons that seem to curve inwards. They may appear rather small compared to convex polygons. The best way to identify a concave polygon is to check for a reflex angle. A reflex angle looks like an obtuse angle, or an arrow cutting into the figure. Concave polygons have reflex angles, convex polygons don’t.
Tags: angle, arrow, concave, curve, Geometry, in, obtuse, polygon, reflex, small
Posted in Geometry | No Comments »
Thursday, November 5th, 2009
Transpose of a Vector Explained
Description
A detailed tutorial on the transpose of a vector. Step by step tutorial including several examples of the transpose of a vector for reference.
Overview
The transpose of a vector is very similar to the transpose of a matrix, because even though the function the operation is being performed on changes, the operation itself doesn’t change. When you transpose a vector, it is just a way of saying the the column of your vector becomes a row, or the row of your vector becomes a column. Transposing vectors is not done very often, but it is still an important part of linear algebra.
Tags: algebra, angle, arrow, change, columns, flip, function, operation, ray, reflect, rows, transpose, vector
Posted in Algebra | No Comments »
Tuesday, October 27th, 2009
Introduction to Hilbert Space
Description
A detailed tutorial on on the application of Hilbert space. Step by step tutorial including several examples of Hilbert space for reference.
Overview
A Hilbert space is commonly used in vector algebra and calculus to generalize the notion of Euclidean space. It is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured. Hilbert spaces are also complete, which is a property that allows enough limits in the space for calculus to be used accurately.
Tags: abstract, algebra, angle, Calculus, complete, Hilbert, inner, length, limit, product, space, structure, vector
Posted in Algebra | No Comments »
Friday, October 23rd, 2009
Overview of the Dot Product
Description
A detailed tutorial of the dot product. Step by step tutorial including several examples of the dot product of a vector for reference.
Overview
The dot product of two vectors always ends up being a scalar. In mathematical terms, this is ![<span style="font-size: x-small;">\mathbf{a}\cdot\mathbf{b}=\left\|\mathbf{a}\right\|\left\|\mathbf{b}\right\|\cos\theta[</span>/latex]. In this case, theta is the measure of the angle between a and b. The definition of a dot product given geometrically is that a and b have a common starting point and that the length of a is multiplied by the component in b that points in the same direction as a. Algebraically, it can be said that [latex]<span style="font-size: x-small;">\mathbf{a} \cdot \mathbf{b} = a_1 b_1 + a_2 b_2 + a_3 b_3.</span>](http://s.wordpress.com/latex.php?latex=%3Cspan%20style%3D%22font-size%3A%20x-small%3B%22%3E%5Cmathbf%7Ba%7D%5Ccdot%5Cmathbf%7Bb%7D%3D%5Cleft%5C%7C%5Cmathbf%7Ba%7D%5Cright%5C%7C%5Cleft%5C%7C%5Cmathbf%7Bb%7D%5Cright%5C%7C%5Ccos%5Ctheta%5B%3C%2Fspan%3E%2Flatex%5D.%20In%20this%20case%2C%20theta%20is%20the%20measure%20of%20the%20angle%20between%20a%20and%20b.%20The%20definition%20of%20a%20dot%20product%20given%20geometrically%20is%20that%20a%20and%20b%20have%20a%20common%20starting%20point%20and%20that%20the%20length%20of%20a%20is%20multiplied%20by%20the%20component%20in%20b%20that%20points%20in%20the%20same%20direction%20as%20a.%20Algebraically%2C%20it%20can%20be%20said%20that%20%5Blatex%5D%3Cspan%20style%3D%22font-size%3A%20x-small%3B%22%3E%5Cmathbf%7Ba%7D%20%5Ccdot%20%5Cmathbf%7Bb%7D%20%3D%20a_1%20b_1%20%2B%20a_2%20b_2%20%2B%20a_3%20b_3.%3C%2Fspan%3E&bg=ffffff&fg=000000&s=0 "<span style=\"font-size: x-small;\">\mathbf{a}\cdot\mathbf{b}=\left\|\mathbf{a}\right\|\left\|\mathbf{b}\right\|\cos\theta[</span>/latex]. In this case, theta is the measure of the angle between a and b. The definition of a dot product given geometrically is that a and b have a common starting point and that the length of a is multiplied by the component in b that points in the same direction as a. Algebraically, it can be said that [latex]<span style=\"font-size: x-small;\">\mathbf{a} \cdot \mathbf{b} = a_1 b_1 + a_2 b_2 + a_3 b_3.</span>")
Tags: algebra, algebraically, angle, common, component, cosine, direction, dot, geometrically, initial, inner, length, mulitplied, point, product, scalar, starting, vector
Posted in Algebra | 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 Find Values of Quadrantal Angles
Description
A detailed tutorial on how to find values of quadrantal angles. Step by step tutorial including several examples of finding values of quadrantal angles for reference.
Overview
Quadrantal angles have a terminal side coinciding with a coordinate axis. A trigonometric functional value of such an angle can be determined by the coordinates of the point where the terminal side intersects the unit circle. When on the unit circle, the Cartesian coordinate (x, y) cooresponds to (cos(&), sin(&)) on the unit circle.
Tags: angle, axis, circle, coordinate, cosine, functional, Geometry, Math, point, quadrantal, sine, terminal, trigonometric, unit, value, x, y
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 »
