Archive for the ‘Trigonometry’ Category
Friday, October 2nd, 2009
Introduction to the Ambiguous Case
Description
A detailed tutorial on the ambiguous case. Step by step tutorial including several example problems of the ambiguous case for reference.
Overview
An ambiguous case is actually any case in mathematics that is open to more than one interpretation, or has more than one solution. There are many different examples of an ambiguous case. However, what most people refer to as the ambiguous case is the Law of Sines. The Law of Sines can use many different techniques to be solved, and those techniques can also be used to figure out if two triangles are congruent.
Tags: AAS, ambiguous, ASA, case, congruent, interpretation, law of sines, Math, SAS, solution, SSS, triangle, trigonometry
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Friday, October 2nd, 2009
Identifying the Cofunction
Description
A detailed tutorial on identifying the cofunction. Step by step tutorial including several examples of how to identify the cofunction for reference.
Overview
In math, we say that a function f is a cofunction of a function g if f(A) = g(B), and A and B are complimentary angles. Cofunctions are very often used with trigonometric functions like sine, cosine, and tangent. If you write a function in terms of its cofunction, it can make it easier to solve certain equations.
Tags: angles, cofunction, complimentary, cosecant, cosine, cotangent, function, Math, secant, sine, tangent, trigonometric function, trigonometry
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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
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Thursday, September 17th, 2009
How to Graph the Sine Function
Description
A detailed tutorial on the solving of the graph of the sine function. Step by step tutorial including several examples of how to solve the graph of the sine function for reference.
Overview
Graphing the sine 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 has points at (0, 0), (pi/2, 1), (pi, 0), (3pi/2, -1), and (2, 0). The x-coordinates are all the main points around the circle while the y-cooridnates are your reference points. The graph of the sine function should resemble a “wave” that starts at the origin and travels in curves going both up and down.
Tags: coordinates, function, graph, graphing, intercepts, Math, reference angle, sine, trig, trigonometry, unit circle, wave, x, y
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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
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Thursday, September 17th, 2009
An Introduction to the Law of Sines
Description
A detailed tutorial on the the Law of Sines and how to prove the Law of Sines. Step by step tutorial including several examples of how to solve problems with the Law of Sines for reference.
Overview
The Law of Sines is a formula that can be used when a triangle has both side and angle measures. The Law of Sines is expressed as:
Where a, b, and c represent the sides, and A, B, and C represent the angles that are opposite of those sides. This formula looks very similar to the Pythagorean Theorem.
Tags: angle, law of sines, Math, side, sine, sine formula, sine rule, sines law, triangle, trigonometry
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Tuesday, September 15th, 2009
How to Use Heron’s Formula
Description
A detailed tutorial on the solving of the area of a triangle using Heron’s Formula. Step by step tutorial including several examples of how to solve for the area of a triangle using Heron’s Formula for reference.
Overview
Heron’s formula is kind of like the Pythagorean theorem for triangles that are not right triangles – although it could also be used with right triangles. However, Heron’s Formula helps you solve for the area, and something called a “semi-perimeter.” Heron’s formula states that:
s = (a + b + c) / 2
Where a, b, and c represent the sides of the triangle and s stands for the semi-perimeter. Once you have the semi-perimeter, you can solve for area using this formula:
A = sqrt[s * (s - a) * (s - b) * (s - c)]
Tags: area, Heron's Formula, Math, precalculus, semi-perimeter, sides, triangle, trigonometry
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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
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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
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