Posts Tagged ‘trigonometry’
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
Posted in Trigonometry | No Comments »
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
Posted in Trigonometry | 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 »
Tuesday, September 22nd, 2009
How to Solve De Moivre’s Theorem
Description
A detailed tutorial on the solving of De Moivre’s Theorem. Step by step tutorial including several examples of how to solve De Moivre’s Theorem for reference.
Overview
De Moivre’s Theorem was named after Abraham de Moivre. It states that any complex number (or any real number) x and any integer n that 
This is called De Moivre’s Formula. This formula is important because it connects complex numbers with trigonometry.
Tags: Abraham de Moivre, complex, de moivre's formula, de moivre's theorem, differential equations, euler's formula, imaginary, induction, Math, numbers, real, trigonometry
Posted in Differential Equations | 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
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
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 »
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
Posted in Trigonometry | No Comments »
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
Posted in Trigonometry | No Comments »
