Posts Tagged ‘cosine’
Thursday, September 24th, 2009
Introduction to the Fourier Series
Description
A detailed tutorial on the solving of Fourier series. Step by step tutorial including several examples of how to solve the Fourier series for reference.
Overview
The Fourier series is very common in differential equations and partial differential equations. What a Fourier series does is decompose a periodic function into the sum of simple oscillating functions, like sine and cosine. Fourier series are part of Fourier analysis and were first introduced by Joseph Fourier to solve the heat equation. So another name for the Fourier series is the heat equation, although they are considered different things. Both the heat equation and the Fourier series are partial differential equations.
Tags: cosine, decompose, differential equations, Fourier analysis, Fourier series, function, functions, heat equation, Joseph Fourier, Math, oscillating, partial differential equations, periodic function, simple, sine, sum
Posted in Differential Equations | No Comments »
Friday, September 18th, 2009
The Tangent Rule and Formula
Description
A detailed tutorial on solving unknown lengths and angles of a triangle using Tangent.
Overview
The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent sides. The formula for tangent is:
Tags: cosine, formula, Geometry, Inside, length, Math, rule, sine, SOHCAHTOA, tangent, triangle
Posted in Geometry | No Comments »
Friday, September 18th, 2009
The Sine Rule and Formula
Description
A detailed tutorial on solving unknown lengths and angles of a triangle using Sine.
Overview
The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. The formula for sine is:
Tags: angle, cosine, formula, Geometry, Inside, length, Math, rule, sine, SOHCAHTOA, tangent, triangle
Posted in Geometry | No Comments »
Thursday, September 17th, 2009
How to Graph the Cosine Function
Description
A detailed tutorial on the solving of the graph of the cosine function. Step by step tutorial including several examples of how to solve the graph of the cosine function for reference.
Overview
Graphing the cosine function is not difficult, but there are a few steps you need to follow. The first is, you need to find all the different points on the graph. You do this by taking a unit circle and using radians and reference points to find all of your coordinates. Then plot your points on the graph, and “connect the dots”. The graph of the sine function should resemble a “wave” That simply goes down once in a big loop and comes back up again.
Tags: coordinates, cosine, function, graph, graphing, intercepts, Math, reference angle, trig, trigonometry, unit circle, wave, x, y
Posted in Trigonometry | No Comments »
Thursday, September 17th, 2009
The Cosine Rule and Formula
Description
A detailed tutorial on solving unknown lengths and angles of a triangle using Cosine.
Overview
The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. The formula for cosine is:
Tags: cosine, Geometry, Math, mathematics, SOHCAHTOA, trigonometry
Posted in Geometry | No Comments »
Thursday, September 17th, 2009
An Introduction to the Law of Cosines
Description
A detailed tutorial on the Law of Cosines and proving the Law of Cosines. Step by step tutorial including several examples of proving the Law of Cosines for reference.
Overview
The Law of Cosines is a formula that is used to relate the sides of a triangle to the cosine of one of its angles. The Law of Cosines can be expressed as:
Where a, b, and c are the sides of the triangle. If the triangle is a right triangle then this simplifies to the Pythagorean Theorem.
Tags: angle, cosine, cosine formula, cosine rule, law of cosines, Math, pythagorean theorem, side, triangle, trigonometry
Posted in Trigonometry | No Comments »
Friday, September 11th, 2009
How to Use SOHCAHTOA
Description
A detailed tutorial on the solving of SOHCAHTOA. Step by step tutorial including several examples of how to solve SOHCAHTOA problems for reference.
Overview
SOHCAHTOA, often spaced out to spell SOH-CAH-TOA, stands for Sine = Opposite/Hypontenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. You use it with an angle to help solve for the sine, cosine, or tangent of that angle. What Opposite, Adjacent, and Hyptonuse stand for are the sides of a triangle – the side exactly opposite your angle, the hypotenuse, and the third non-hypotenuse side that is next to your angle. Because of this, SOHCAHTOA can only be used with a right triangle. The values for opposite, adjacent, and hypotenuse are the length of the side of the triangle it stands for. It is not necessary to know the measure of the angle before using SOHCAHTOA.
Tags: adjacent, angle, cosine, Geometry, hypotenuse, length, Math, opposite, right triangle, side, sine, SOH-CAH-TOA, SOHCAHTOA, tangent, triangle, trigonometry
Posted in Geometry, Trigonometry | No Comments »
Thursday, September 10th, 2009
Trigonometric Identities Explained
Description
This video is a review of all the important trig identities. It provides several examples of different trig identities and shows when and how you would have to use them. This video provides content in an organized manner.
Overview
Trigonometric identities, or trig identities, are equations dealing with trig functions that should be memorized. The most common trig functions are sine, cosine, and tangent. Trig identities will help you when you need to simplify equations with trigonometric functions in them. There are a few very important trig identites. Two of these are the Pythagorean trig identity and the Ratio identity.
Pythagorean Trig Identity: 
Ratio Identity: 
From the Pythagorean trig identity, another identity can be found. This is 
. There are a few other identities, that are not so much trig identities as factoring for trigonometric functions.
sin(a + b) = [sin(a) * cos(b)] + [sin(b) * cos(a)]
cos(a + b) = [cos(a) * cos(b)] – [sin(a) * sin(b)]
sin(2a) = 2 * sin(a) * cos(a)
cos(2a) = [cos(a)]^2 – [sin(a)]^2
There are many more trig identities, but these are the most important. With these, you will be able to find almost every other trig identity.
Tags: cosine, Math, pythagorean, pythagorean trig identity, ratio identity, sine, tangent, trig, trig identities, trigonometric equations, trigonometric function, trigonometric identities, trigonometry
Posted in Trigonometry | No Comments »
Friday, September 4th, 2009
How to Solve Derivatives with Trigonometric Functions
Description
This video shows the basic trigonometric functions and their derivatives. Content is laid out in an organized and easy to follow manner.
Overview
Trigonometric functions, also known as just trig functions, are very common – they are sine, cosine, tangent, secant, cotangent, cosecant. These are derivatives that you should have memorized, because there is no good way to solve for them.
d/dx sin(x) = cos(x)
d/dx cos(x) = -sin(x)
d/dx tan(x) = sec^2(x)
d/dx sec(x) = sec(x) * tan(x)
d/dx csc(x) = -csc(x) * cot(x)
d/dx cot(x) = -csc^2(x)
Tags: Calculus, cosecant, cosine, cotangent, derivative, derivatives, differentiation, Math, secant, sine, tangent, trig, trig functions, trigonometric, trigonometric functions, trigonometry
Posted in Calculus | 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 »
