The Basics of Trigonometry


Trigonometry is a field of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. Though many modern students who pursue this career are unaware of its history, it has always been important to engineers. Pythagoras, the Pythagorean Theorem and Archimedes’ The Great Bridge are just a few of the timeless concepts that the mathematics of triangles can be applied to. Trigonometry has two primary components: arithmetic and geometry. Geometry describes geometric relationships between lines and angles. Arithmetic is the study of multiplication, division, integration, and multiplication

Trigonometric Ratios

You'll start learning about trigonometry by studying ratios—sizes of the various areas in a triangle. Because we need to know the lengths and angles of the triangles so we can measure them, we have to find the ratios between the sides of each triangle. As we learn about ratios, we'll see that the lengths and angles of each side of a triangle have a relationship to each other, and to the sides of a third triangle, which we'll also need to make and compare. In other words, we want to know what the hypotenuse (the other side of the triangle) and the other two sides of the triangle (the sides opposite the other two sides of the triangle) are. A. The Pythagorean Theorem All three sides of a triangle have the same length if the square of the opposite side is 1.

Functions of Sine and Cosine

On top of being useful for math equations, trigonometry also works as a useful skill for everyone who uses an iPhone and uses the calculator app. On their own, sin and cosines are not very complicated operations. In the first step, you need to know how to understand what a “sin” and a “cosine” is, and what the corresponding ratios are. Trig, the technical name for trigonometry, is based on two other Greek terms that are called “a sinus” and “cose.” In physics, a sinus refers to the central or resonant peak of a vibrating system, and cose refers to the amplitude of a vibration. To find the volume of a system, the sinus is divided by the cose, and this measurement becomes a measure of the dimensions of the system. In trigonometry, these measurements are called “a sinus” and “a cosine.

Functions of Tangent and Cotangent

To begin with, let’s review some important concepts in trigonometry. Tangent Tangents are a function of one side of a triangle. The tangent at any point in a triangle will tell you how much the length of the opposite side is away from the tangent line. In other words, if you are on one side of a triangle, then the tangent to that side will tell you how far from the perpendicular your other side is. For example, if you are on one side of the triangle and the opposite side is located about 10 feet away from you on the other side, the tangent would be zero (that is, it is zero from one side to the other). If your original side is 30 feet away and your opposite side is 5 feet, then the tangent would be zero.

Applications of Trigonometry

To better understand how tridimensional triangles relate to angles, let's make some triangles. Triangle area of triangle with area 2 2 + (sin + cos) 2.6 Triangle area of triangle with area 2 2.6 Right triangle with area = [(sin - cos) 2.6)2 Triangle area of triangle with area = [(sin - cos) 2.6)2 Triangle area of triangle with area = [(sin - cos) 2.6)2 Triangle area of triangle with area = [(sin - cos) 2.6)2 Triangle area of triangle with area = [(sin - cos) 2.6)2 The two triangles with equal areas and side lengths are identical. Since angles between sides and lengths are one another, they must also have the same area. And the two triangles with equal angles and sides are identical. Since angles between sides and lengths are one another, they must also have the same area.

systems of linear equations

Systems of Linear Equations

Systems of Linear Equations

In mathematics, a system of linear equations is a collection of one or more linear equations involving the same set of variables. The intersection point is the solution.

Solving Linear Systems

To solve a linear system, one simply has to divide each linear equation by the sum of the other variables in order to find the solution. This is done by substitution. There are two different equations used to find the solution for linear systems of three variables. The first equation is usually referred to as the explicit system of linear equations or equations A + B = C. The second equation is the implicit system of linear equations or equations A + B = C. In the explicit system, each variable is assigned a fixed value. For example, in the explicit system A equals 1, whereas in the implicit system, each variable has a variable value depending on which variable is being used to represent that variable.

Linear Systems in Three Variables

As you might expect, one of the most basic concepts of calculus involves the intersection of planes. A plane is defined as a three dimensional circle drawn on the plane defined by the three variables. The intersection point is the solution. Knowing that the intersection point of a plane is the solution, we can see that solving systems of linear equations using the intersection of three variables is the same as solving three plane equations. You can solve planes through the intersection of three variables by taking the derivatives. This is a single step process. In the world of math, a derivative of a function means the change in value as a function changes. An example would be a line in the plane that is bisected. That bisection creates two new lines.

Graphing Linear Systems

In trigonometry, graphs of linear systems are known as planes. Planes are three dimensional. Linear systems in Cartesian coordinate systems: The formula for constructing a plane is as follows: Consider a plane and find the linear equation between the origin of the plane and the point it divides into two. The above formula determines an invisible line, also known as a dot. The number of parallel lines passing through the origin of a plane is defined as the hypotenuse of the line. The formula for constructing a plane is as follows: Let the two equations of the plane be Let t be the length of the line and x and y be the number of such lines passing through the origin. There is one and only one solution to this system of equations.

Complex Solutions

The simplest linear equations involve real and imaginary parts of a variable, in addition to zero. The first example is the straight line equation of a line, E = 2. So the solution is 2. The second example is the equation for an ellipse, f = a + b, where a, b, and a*a are the coordinates of the ellipse. The solution is (1+b)/a. In addition, a and b are both unknown. The ellipse has two unknowns, the coordinates of the center and radius. A and b are the coordinates of the center and the radius, respectively. In addition, a and b are both unknown. The solution is the complex number (2a2b) + (1a2b), which is the distance (a*b) to the center. As long as two variables are either real or imaginary, linear systems can be solved.


Knowledge of how to solve linear equations is a powerful tool in your arsenal. Solving linear equations is part of many core mathematical education requirements, and I think it’s worth studying. You might even be able to write an article for me. Enjoyed this lesson? Look into Learning Algebra: Quick, Simple, and Easy Systems of Equations. It is perfect for students just starting their math education!


What is a semiconductor?


Silicon is a pure element, but a semiconductor is defined as any material which can conduct electricity. It would be possible to be a conductive metal, such as gold, but this is not a semiconductor. All materials which conduct electricity are semiconductors and all materials which do not are non-semiconductors. Cadmium Sulfide is a semiconductor, as is Gallium Arsenide and Gallium Nitride Electronic Devices Semiconductors are the heart of modern electronics. They are key components in all computing, telecommunications, radar, and guidance systems for missiles and aircraft. The transistor and vacuum tube are other very important components of electronics and are found in computers.

The types of semiconductors

Semiconductors can be of many different properties: Alkali (e.g. Na, K, Ca, Mg, etc.) Sulfur Amino (e.g. As, Cd, Mo, etc.) Boron Cobalt Sulphur diode (at right) Organic light-emitting diode (OLED) Lead selenide – the light on an OLED seems to follow the outline of the silver conductor, which is the rare earth metal tin Vacuum tube (valve) transistors – on a non-silicon silicon chip, light travels through electrons (vacuum tubes) and through a switch (transistor). Today, silicon is the most common semiconductor, as it is easier to work with and its properties are best understood. Other semiconductors which have many different properties are gallium arsenide, indium phosphide, indium phosphide – infrared photodetector, aluminum nitride, indium tin oxide, etc.

How do semiconductors work?

In the simplest form of semiconductors, metals and non-metals conduct electricity without any other chemicals involved. On the other hand, semiconductors that are conductors will do this via specialised molecules which conduct electricity at the same time as they carry electrical charge. The electricity carries the charge across the conductor, and the mobile molecules carry the electrical charge out of the conductor. Because the electrical current carrying charge passes over the conductor, and the electrons from a semiconductor do so at a specific velocity, the conductivity of the material is related to its Joule heating. This is one of the reasons that metals and semiconductors are so widely used in the production of electronic devices.

Who uses semiconductors?

Semiconductor Devices Semiconductor Devices are used for making many things such as components of electronic circuits (such as transistors and diodes), photovoltaic cells (converted by silicon), and laser diodes (sparked by the light of the radiation they emit). Semiconductor devices can also be used for making radio transmitters and receivers, cellular phone receivers, video game consoles and so on. What can I do with a semiconductor? Depending on the type of device (or area) being used, you could be looking at any of the following things. The main things that you will be looking for in a circuit are voltage, current, and power. Semiconductor Devices Components of Electronic Circuits Transistors: Transistors control the flow of current in electronic circuits.


The process of film forming a semiconductor is fairly simple in principle, and a new technique has been developed which makes the entire process accessible to beginners. The theory in terms of the physics of the process and the corresponding physical modelling is not complex, and the development of the necessary materials for the process has been carried out by many research groups. The systems that have been developed for the manufacturing of these wafers are also available commercially, although the costs have tended to be higher than those of the conventional technique. Theoretical understanding and modelling is also a prerequisite for improving the quality of the structures produced by the method.

heat and mass transfer

heat and mass transfer

Heat and Mass Transfer: The Fundamentals

Heat and Mass Transfer

Heat and Mass Transfer is a serves the circulation of new developments in the field of basic research of heat and mass transfer phenomena, as well as related material properties and their measurements.

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What are heat and mass transfer?

Heat and mass transfer are commonly referred to as the processes by which an electric current (electromotive force) is applied to an external mechanical force and resulting heat is transferred from one body to another. A high voltage electrical circuit generates a low mechanical force. Heat transfer (also known as heat conduction) from a body to another is required to reach the object at a high temperature. The applied electrical voltage generates heat at the contact area between two material bodies. About the journal Published quarterly by Springer Nature, the journal features reviews, original papers, articles from leading scholars, conference abstracts, case studies and a dynamic communications area.

Fundamentals of thermal physics

Issued six times a year in print and online Issue Three - Heat and Mass Transfer

Fundamentals of fluid mechanics

The fundamental principle of fluid mechanics is that fluid motion is governed by mass conservation and pressure conservation, whereas surface friction provides a method of removing individual particles from fluid flow. This article provides a succinct outline of the diverse properties of fluids that we deal with in our everyday lives. To begin, we will briefly discuss the Navier-Stokes equation, which is considered the key analytical tool in fluid mechanics. The Navier-Stokes equation, which was introduced in 1807 by the French mathematician and physicist Émile Léonard de Villefière, explains how, at any given time, fluid flows over a surface in a manner that preserves the product of the speed of movement and the force of gravity.

Fundamentals of mass transfer

The conceptual science of mass transfer comprises mechanical, thermal and convective phenomena. These are used for convective cooling in low temperature systems, for heat transfer in large heat capacities and for cold plasmas. Generally, the physical phenomena of mass transfer can be divided into four main categories: static mass transfer, dynamic mass transfer, turbulent mass transfer and heat conduction. Dynamic mass transfer occurs in high temperatures, where fluid particles move through a medium and are influenced by the shear, capillary, radial and viscous forces. Sometimes, fluids at low temperature can also be considered as the solution to the equation of state of the fluid.


Time and time again we have found that funders are not looking for science-based results. Instead, they look for a “high impact” study. As we continue to see, money doesn’t determine research quality. In the pursuit of a high impact study, institutions like RPI rely on questionable science. Instead of working towards making a positive change in society, they are choosing to dig into relationships between race and blood test results. Is there a place for toxicology at RPI? Is there a need for true research that will improve the quality of life of the students? The answer is “No.” It’s time to bring real science back to the undergraduate science community. Let’s work towards producing results that are both well respected and effective.

operations management

Operations Management

The Crucial Role for Operations Management in Business

Operations Management

What is Operations Management

Operations management is an area of management concerned with designing and controlling the process of production and redesigning business operations in the production of goods or services. In the past, this area of management was under the umbrella of organizational studies. However, with the rapid technological changes that organizations experience, the application of operations management has had to adapt to those changes as well. The increased emphasis on control of processes is based on several principles that are based on well-defined management requirements. These requirements range from the control of costs to the control of factors such as quality, compliance, security, and customer satisfaction.

Examples of Operations Management in the Workplace

Based on reports on operations management, you can see examples of operations management in the workplace. Companies are using an operations management framework to maximize their employees' productivity, to increase customer satisfaction, and to protect their business reputation. Some examples of companies using operations management are: Baxter Healthcare – Baxter Healthcare is one of the largest manufacturers of small molecule injectable pharmaceuticals. According to company reports, over 90% of Baxter's total net sales come from its seven core products: insulin, blood collection systems, pediatrics devices, joint and back pain treatment devices, intraosseous needle systems, small bowel pumps, and other therapeutic and surgical devices.

The Role of Operations Management in Business

Operations management is an area of management concerned with designing and controlling the process of production and redesigning business operations in the production of goods or services. In addition, it also gives assurance to management about how a business operation is performing and what is the optimal point at which a business needs to be operated. The challenge with most organizations is that they have multiple processes in the production and delivery of their goods or services. This makes it almost impossible for management to give a precise picture of their business operation. They have to work in a situation where they have incomplete information and incomplete visibility of what is going on in their business.


The modern trend in Business management is moving towards greater use of information technologies such as cloud computing, big data analytics, social media and many others. One area of greater use of Information Technology is in information systems that support the operations. Among these, operations management is an area that has seen an important increase in importance. Operations management is critical for efficient production and delivery of services in a growing global economy and is becoming a critical area of business management.

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nuclear physics

Nuclear Physics The Basics of Atomic Structure and Reactions

Nuclear Physics

Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions; Nuclear physics should not be confused with atomic physics, which studies the atom as a whole, including its electrons.

What is Nuclear Physics?

For The simplicity way, we will consider the nuclear particle as a positively charged nucleus. This nucleus is surrounded by positively charged protons and negatively charged neutrons. Electrons reside on the outer edge of the nucleus, interacting primarily with the nucleus's electromagnetic field, as well as electrons in the nucleus. A nuclear particle may have one, two, three, or more nuclei around it. Each of these nuclei can be protons, or they can be either positively or negatively charged. The nuclear particle is considered to be moving due to its electromagnetic fields. A nucleus may exist in three different states: a fission (fusion) nucleus, a nucleus with a partially fissioned (split) core, or an intact core.

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Types of Nuclear Reactions

The different kinds of reactions that may take place in a nucleus are the following: Conversion between nuclei Nucleophilic substitution Nucleophilic addition Nucleophilic deamination Hydrogen activation Particle-Nuclear Force Nuclear Reactions in the Body In biology, a reaction is a process that allows the chemical bonds of an organic molecule to be altered. Nucleophilic Substitution Nucleophilic substitution is when two or more nuclei are able to attach to one another due to the effects of positive or negative charges. The "two" or "two and one" in "two nucleophilic substitution" means that there is a positive charge on one nucleus (cobalt) and a negative charge on another (iron).

The Atomic Structure

Here are a few basic facts about atoms: Atomic particles are particles that are smaller than a millionth of a meter in size. Atoms are extremely small — about the size of a beam of light. Atoms are made up of smaller particles called protons and neutrons. The number of protons and neutrons in an atom depends on the chemical element it is made of. The number of protons and neutrons in an atom depends on the type of atom it is made of, for example, the number of protons in a carbon atom is about 14. Each atom consists of one or more electrons. The electrons are positive particles that move around the atomic nucleus. A simple atom is made up of an atom with just a single nucleus and an equal number of electrons orbiting the nucleus.


If you are seriously considering a career in nuclear engineering or nuclear medicine, first look into internships or volunteer programs at universities that have nuclear research laboratories. Also, make sure you get a good education, which can be aided by taking classes online or attending classes in person. Follow your passion for the field and your curiosity about the world, and you will be on your way to a successful career.

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gravitational magnetic electric field

Gravitational Magnetic Electric Eield

What Is a Gravitational Magnetic Electric Field: One of the Great Mysteries of Physics

Gravitational Magnetic Electric Field

What is a gravitational magnetic electric field?

Ever since astronomers observed Jupiter's magnetic fields in the 1950's they wondered if there might be another kind of field that may appear only in connection with large celestial bodies. In fact, since 1977 there has been a large group of astronomers and cosmologists that have been working together to answer the question of the existence of gravitational magnetic fields. The latter have puzzled for more than 40 years how it is possible that these fields would have such a large magnitude compared to the mass-to-energy ratios (see below). Since the 1970s, there have been reports that Jupiter and Saturn have magnetic fields with the magnitude of a thousand Earths, approximately a factor of 30 stronger than the terrestrial fields.

What are the basic principles behind it?

The force was originally discovered by Albert Einstein and found by Franklin and Rayleigh in the 19th century, and soon after, August Kekulé von Stradonitz discovered that if a magnetic field were applied to a conductor like a wire, the material would become polarized. Kekulé also discovered that if you applied a magnetic field to a magnet, it would rotate and that the direction of rotation depended on the strength of the field. It is this famous pencil line created by a human hand in wood-which was originally discovered by Galileo and shown by Kekulé to be the effect of a magnetic field (due to the perpendicular movement of the magnet) – that is the foundation for our theory of magnetism. In today’s world, we understand how it works for motors, magnetic bearings, and machines.

How does it function?

The Sun and most other known stellar objects produce much weaker magnetic fields. The cosmic microwave background also does not have a strong magnetic field and may not have a field even if the Universe were infinite. However, stellar bodies like the Sun have magnetic fields because they are predominantly made up of magnetic elements (or atoms), such as iron or nickel. By adding to these stellar magnetic elements, the rate of addition determines the strength of the magnetic field. This is the same process that produces Earth’s magnetic field. How is it generated? Such field-generating events must be highly energetic, and it is proposed that large binary stars merge and produce a large (though faint) gamma-ray burst, which in turn generates a strong magnetic field.

Why is it important today?

In 1909 J. Thomson determined that an electric field could produce a gravitational field, and this led to the idea that two oppositely facing electric charges, like the Earth and the Sun, could attract each other. This event was interpreted to be the cause of the movement of the planets around the Sun. In 1913 George Gamow found that the electron is affected by electromagnetic fields and moved like an electric current. He showed that this was the first demonstration of the existence of the electromagnetic field. Einstein showed that this magnetic field could affect light waves by refraction, bending, and diffusing them, and thereby altering the frequencies of the light.


Some particle physicists are considering the possibility that the world’s first teleportation machine has been discovered at Fermilab. If it was, then this would resolve the vast majority of major outstanding problems. Here’s a list of these major mysteries: Lattice Relativistic Quantum Field theory. Modular lattice QCD. Standard Model of particle physics. QCD model and the Short-Baseline Interferometry experiment at the LBNL. Laser Scattering of Solid Matter in Cold Plasma at the LBNL. Physics of Quantum Gravity. Young Universe Model. Higgs Boson (unlike all other major objects, had a mass equal to -1/r. In other words, matter (i.e., mass) makes up only 1/r of the universe, the rest is dark energy. Gravitational Insanity.

Pythagorean Theorem and How Does

pythagorean theorem

Pythagorean Theorem

What is the Pythagorean Theorem and How Does it Work?

Pythagorean Theorem

What is Pythagorean Theorem?

The theorem was first proved by Pythagoras about 5,500 years ago, but only since 1900, over 200 years have been known about the theorem. Many religions base their interpretations on the Pythagoras theorem; for example; the Hindu religion and Jainism believes in this theorem.

The Pythagorean Theorem has been considered the best mathematical theory that one can use in the construction of astronomical and geographical models and it can be used to calculate any mathematical function.

Suppose we start with a triangle (ABCDE) with each side 1, and each of the angles 3.5, and then we take the square of the hypotenuse: {A: 1/3.5, B: 1/3.5, C: 1/3.} In this case the hypotenuse is 3, so the square of the hypotenuse is {3/3.5} We can now calculate the square of the other two sides to: {2: 1/3.

How does it work?

Pythagoras theorem can be put into perspective by looking at a right angled triangle. If we would cut a straight line through any of the four sides of this triangle, we will find that it is the longest straight line.

Pythagoras theorem is an interesting formula that works with triangles. In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides Pythagoras theorem has been proven wrong by Galileo, they thought that the length of a straight line can be approximated with a constant number called the tangent.

But recently they have found out that the length of a straight line could be approximated by a constant number called the cosine. Galileo came up with this formula and named it the Pythagorean theorem.

Why is it important?

The geometric figure of a right triangle is useful because of two properties.

First, every right triangle has the same isosceles triangle theorem. This means if you draw a right triangle on a piece of paper, you will get the same triangle on the opposite side of the paper, so long as it is a right triangle.

And second, if you draw a right triangle, and let two of the sides be the lengths of the hypotenuse and the other two the lengths of the base, then your figure will have the square of the sum of squares of the other two sides. This is also known as Pythagoras’ theorem. Pythagoras theorem: x2 + y2 = y2 + x How does it work?

Who Else Used It?

More than what we can think of, many greats of history have been linked to this theorem. The names of some of the earliest known Pythagorean Theorem was Robert Recorde (1360-1437) and is attributed to Fibonacci. Though, it was most famously used by Leonardo da Vinci, who is considered to be the most famous mathematician in history.

What are some of the Plimpton elements used in Physics? You know, a Plimpton element are “all the generalizations, which apply to the physical case of a system having an action involving vectors“.

These are the “accelerated versions of Newton’s laws of motion and his inverse dynamics (i.e., the interaction of forces and resultant effects between forces). Most of them can be seen in the article Plimpton's Elements of Mechanics.


In this article, we have learnt how to calculate the length of a given triangle with the help of trigonometry. We have also learned that Pythagoras’ theorem can be used to find the total length of a triangle and that all Pythagorean triangles have the same total length.

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collision theory

Collision Theory

Collision Theory

Introduction to collision theory

There are many ways to achieve change in a system of matter, and a common way to achieve change in a system of matter is through a collision. There are several types of collisions; however, these commonly fall into one of two categories: One collides with the reactant only, while the other collides with both the reactant and the reaction product. Here is a picture of what happens when one type of collision happens, called a neutron scattering. In this photo, the reactant is the black line and the reaction product is the red line. The neutron line is the result of a neutron interacting with both the reactant and the reaction product (molecules of reactant-gas). The neutron becomes heated by the reaction, and continues to travel along the reaction line with a temperature.

How collision theory works

In collision theory, two colliding particles can be classified as ‘winner’ and ‘loser’ as: Winner In this case, the winner is the one that gets the momentum shift. Loser In this case, the loser is the one that loses the momentum shift. Why does collision theory work? Collision theory is thought to work on the following basis:

  • 1. A one dimensional structure that is required to determine if a collision is or is not successful.
  • 2. A function is considered as zero or one if there is no kinetic movement during a collision.
  • 3. The product of these two definitions: V = k 1/a = 0.0 or V = k 1/a = -k 1/a. Collision theory can help to develop certain classifications or hypotheses:

Applications of the collision theory

Optical Characterization of Chemical Reaction Chemical Mixtures Manipulating chemical mixtures in a controlled manner. Relatively simple and efficient methods of characterizing molecular flow and mixing in a controlled manner.


To grasp the significance of this information, consider the meteor that hit Chelyabinsk, Russia. According to CNN, it was a whopping 59 miles per hour. Some chemical reactions, such as water burning, take several seconds to produce visible fires. These reactions would not result in detectable visual changes if a low enough temperature is reached, so Chelyabinsk was nearly perfect. The following are statistics that show what chemical reaction takes place to make the impact temperature a fraction of a degree; the base definition of a fraction is any number less than one. There were 20 events measured in 2009. Just four had lower than a one percent chance of occurring in a single occurrence over a thirty year period.


The Basics of Trigonometry Trigonometry is a field of mathematics that studies relationships between side lengths and angles of triangles....