Posts Tagged ‘radians’
Thursday, November 19th, 2009
Defining the Angles Between Vectors
Description
A detailed tutorial on how to define the angles between vectors. Step by step tutorial including several examples of angles between vectors for reference.
Overview
In general, it is easier to find the angle between 2D vectors, rather than 3D vectors. In order to define the angles between vectors, we need to use the dot product in conjunction with a few other functions. The angles between vectors can be expressed as angle = arccos(v1xv2), where v1xv2 is how the dot product is expressed.
Tags: 2D, 3D, absolute, algebra, angle, arccos, conjunction, cosine, define, degrees, dot, function, linear, magnitude, product, radians, value, vector
Posted in Algebra | No Comments »
Friday, October 2nd, 2009
How to Find the Reference Angle
Description
A detailed tutorial on finding the reference angle. Step by step tutorial with several examples of how to find the reference angle for reference.
Overview
The reference angle is something you run into in precalculus and calculus. The reference angle is only used when working with radian measure, which while being more precise than degree notation, can sometimes be difficult to figure out and out into something you can use when solving an equation. The reference angle uses the unit circle, which has four points of 0, pi/2, pi, 3pi/2, and 2pi. When calculating an angle that is not exact, you place it on your unti circle and find the closest of those points. Subtract them. This is your reference angle.
Tags: Calculus, degrees, Math, pi, radians, reference, reference angle, subtract, unit circle
Posted in Calculus | No Comments »
Thursday, October 1st, 2009
Definition of the Spiral of Archimedes
Description
A detailed tutorial on the Spiral of Archimedes. Step by step tutorial including several visual examples of the Spiral of Archimedes for reference.
Overview
The Spiral of Archimedes, also known as the Archimedean Spiral and the arithmetic spiral, is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity. It is represented by the equation 
The variable a controls which direction the spiral turns in, and the variable b controls the distance between successive turnings. We would recognize the Spiral of Archimedes as being an ordinary spiral that is often used to express the unexplained in movies and television.
Tags: angular velocity, Archimedean Spiral, arithmetic spiral, Calculus, logarithmic spiral, Math, polar coordinates, radians, spiral, Spiral of Archimedes
Posted in Calculus | No Comments »
Tuesday, September 29th, 2009
Definition of a Hypocycloid
Description
A detailed tutorial on the definition of a hypocycloid. Step by step tutorial including a visual example of the definition of a hypocycloid for reference.
Overview
A hypocycloid is not really an equation, or a graph, or any true function. A hypocycloid is simply a representation of the edge of a wheel or other circular item rolling on the inside of a circle to form curves. What is more noticeable than the curves it forms is the shape enclosed by the curves, which is almost like a stretched out diamond. This stretched out shape is the real hypocycloid.
Tags: brachistochrone problem, Calculus, circle, circular wheel, curves, cycloid, epicycloid, hypocycloid, Math, parameter, polar coordinates, polar graph, radians, roulette, round, tautochrone problem, The Helen of Geometers
Posted in Calculus | No Comments »
Tuesday, September 29th, 2009
Definition of an Epicycloid
Description
A detailed tutorial on the definition of an epicycloid. Step by step tutorial including a visual example of the definition of an epicycloid for reference.
Overview
An epicycloid is not really an equation, or a graph, or any true function. An epicycloid is simply a representation of the edge of a wheel or other circular item rolling along the edge of a circle to form curves. The curve it forms is really several concave down curves side by side, in a circular pattern.
Tags: brachistochrone problem, Calculus, circle, circular wheel, curves, cycloid, epicycloid, hypocycloid, Math, parameter, polar coordinates, polar graph, radians, roulette, round, tautochrone problem, The Helen of Geometers
Posted in Calculus | No Comments »
Tuesday, September 29th, 2009
Definition of a Cycloid
Description
A detailed tutorial on the definition of a cycloid. Step by step tutorial including a visual example of the definition of a cycloid for reference.
Overview
A cycloid is not really an equation, or a graph, or any true function. A cycloid is simply a representation of the edge of a wheel or other circular item rolling in a straight line to form curves. The curve it forms is really several concave down curves side by side.
Tags: brachistochrone problem, Calculus, circle, circular wheel, cycloid, Math, parameter, polar coordinates, polar graph, radians, roulette, tautochrone problem, The Helen of Geometers
Posted in Calculus | No Comments »
Tuesday, September 22nd, 2009
How to Solve Euler’s Formula
Description
A detailed tutorial on the solving of Euler’s Formula. Step by step tutorial including several examples of how to solve Euler’s Formula for reference.
Overview
Described as one of the most beautiful and important mathematical formulas of all time, Euler’s Formula is something that is essential to know about. It is written in the form of 
where x is typically given in radians, although it can also be a complex number. Euler’s Formula is named after Leonhard Euler, who was not the first one to discover the formula, but to put it in the form we know today.
Tags: complex, complex analysis, euler's formula, imaginary, Leonhard Euler, Math, radians, trigonometry
Posted in Differential Equations | No Comments »
Thursday, September 3rd, 2009
How to Convert Degrees into Radians
Description
This video gives an in-depth tutorial on how to convert degrees to radians, and how to convert radians back into degrees. Many examples are provided and explanations are set up in an easy to understand fashion.
Overview
Degrees are a very common thing to see – they are used in solving angles, and sometimes used in solving trangle problems. However, degrees are only a unit, and like any unit they can be converted to another one. Degrees are converted to radians – radians are used with sine, cosine, and tangent. The easiest way to remember radians is to memorize the most common degrees and their conversion into radians:
0 degrees = 0 radians
30 degrees = pi/6 radians
45 degrees = pi/4 radians
60 degrees = pi/3 radians
90 degrees = pi/2 radians
Tags: angles, cos, cosine, degrees, Math, pi, radians, sin, sine, tan, tangent, triangles, trigonometry
Posted in Trigonometry | No Comments »
