Applications of trigonometry in real life

By clicking “Submit,” you agree to receive recurring advertising emails, text messages and calls from Mathnasium and its independently owned learning centers about our offerings to the phone number/email provided above, including calls and texts placed using an automatic telephone dialing system. Consent to receive advertising text messages and calls is not required to purchase goods or services. By clicking “Submit,” you also consent to Mathnasium's Terms of Use and Privacy Policy. Trigonometry is a very different subject than most of the math we encounter in our lives previously, and it takes a different way of thinking to understand. For that reason, many people just want to get it over with when trig comes up in school. This article from enbibe (Source:https://www.embibe.com/exams/real-life-applications-of-trigonometry/ ) explains how useful trigonometry can be in a wide range of real-life applications! Trigonometry simply means calculations with triangles (that’s where the tri comes from). It is a study of relationships in mathematics involving lengths, heights and angles of different triangles. The field emerged during the 3rd century BC, from applications of geometry to astronomical studies. Trigonometry spreads its applications into various fields such as architects, surveyors, astronauts, physicists, engineers and even crime scene investigators. Now before going to the details of its applications, let’s answer a question have you ever wondered what field of scienc...

Trigonometry, the branch of mathematics that describes the relationship between the angles and lengths of triangles, helped early explorers plot the stars and navigate the seas. Nowadays, trigonometry is found in everything from architecture to zigzag scissors. While it may seem as if trigonometry is never used outside of the classroom, you may be surprised to learn just how often trigonometry and its applications are encountered in the real world. Much of architecture and engineering relies on triangular supports. When an engineer determines the length of cables, the height of support towers, and the angle between the two when gauging weight loads and bridge strength, trigonometry helps him to calculate the correct angles. It also allows builders to correctly lay out a curved wall, figure the proper slope of a roof or the correct height and rise of a stairway. You can also use trigonometry at home to determine the height of a tree on your property without the need to climb dozens of feet in the air, or find the square footage of a curved piece of land. Music Theory and Production Trigonometry plays a major role in musical theory and production. Sound waves travel in a repeating wave pattern, which can be represented graphically by sine and cosine functions. A single note can be modeled on a sine curve, and a chord can be modeled with multiple sine curves used in conjunction with one another. A graphical representation of music allows computers to create and understand sou...

\( \newcommand\) • • Focus Questions The following questions are meant to guide our study of the material in this section. After studying this section, we should understand the concepts motivated by these questions and be able to write precise, coherent answers to these questions. Let \(A, B, C\), and \(D\) be constants with \(B > 0\) and consider the graph of \(f(t) = A\sin(B(t - C)) + D\) or \(f(t) = A\cos(B(t - C)) + D\). • What does frequency mean? • How do we model periodic data accurately with a sinusoidal function? • What is a mathematical model? • Why is it reasonable to use a sinusoidal function to model periodic phenomena? In Section 2.2, we used the diagram in Figure \(\PageIndex\) is one-quarter of a period. In Progress Check 2.16, we will use some of these facts to help determine an equation that will model the volume of blood in a person’s heart as a function of time. A mathematical model is a function that describes some phenomenon. For objects that exhibit periodic behavior, a sinusoidal function can be used as a model since these functions are periodic. However, the concept of frequency is used in some applications of periodic phenomena instead of the period. Definition The frequency of a sinusoidal function is the number of periods (or cycles) per unit time. A typical unit for frequency is the hertz. One hertz (Hz) is one cycle per second. This unit is named after Heinrich Hertz (1857 – 1894). Since frequency is the number of cycles per unit time, and the...

Amongst the lay public of non-mathematicians and non-scientists, Thomas Paine's statement [ ] In Chapter XI of The scientific principles that man employs to obtain the foreknowledge of an eclipse, or of any thing else relating to the motion of the heavenly bodies, are contained chiefly in that part of science that is called trigonometry, or the properties of a triangle, which, when applied to the study of the heavenly bodies, is called astronomy; when applied to direct the course of a ship on the ocean, it is called navigation; when applied to the construction of figures drawn by a ruler and compass, it is called geometry; when applied to the construction of plans of edifices, it is called architecture; when applied to the measurement of any portion of the surface of the earth, it is called land-surveying. In fine, it is the soul of science. It is an eternal truth: it contains the mathematical demonstration of which man speaks, and the extent of its uses are unknown. History [ ] Great Trigonometrical Survey [ ] This section does not Please help Find sources: · · · · ( August 2019) ( Scientific fields that make use of trigonometry include: That these fields involve trigonometry does not mean knowledge of trigonometry is needed in order to learn anything about them. It does mean that some things in these fields cannot be understood without trigonometry. For example, a professor of In some of the fields of endeavor listed above it is easy to imagine how trigonometry could be ...

\( \newcommand\) • • • • • • • • • • • • • • • Use a calculator to find sine, cosine, and tangent in basic applications Work it Out 1 Two students, Manny and Julisa, were having a debate about the how to model the wavelength of their school's radio station frequency. To simplify their debate, they used another model of a wave as shown below. Figure \(\PageIndex\right)\) and Julisa says it is \(f(x)=5 \cos x\). • Without graphing the equations, can you tell which student is correct, and if so, who? • How do you know? • What would the graph of the incorrect equation look like when compared to the graph above? Discussion Recall that the equation for a cosine function is \(y=A\cos(w(x−h))+k\) where \(A\) changes the But is it a cosine function like Julisa believes, or a sine function with a shift in the phase like Manny believes? If you graph these two functions, and also \(y=5 \sin x\) you will see the subtle, but important differences between the three graphs. Work it Out 2 Figure \(\PageIndex\) The amplitude of the function of the co-height is 50 because the car will range between +50 and -50 feet away from a vertical line (like the \(y\)-axis) going through the center of the Ferris wheel. Therefore, the co-height can be represented by the function \(f(\theta )=50 \cos(\theta)\). Don't forget: you still need to create a graph and find the function for the height of Car 1. Example \(\PageIndex\) The above is a graph of the function \(Y(\theta )=50 \sin \theta +60\). Work it ...

One example of an inverse trigonometric function is the angle of depression and angle of elevation. I believe these two fit as a plausible example because they use sine or cosine or tangent in order to determine the angle of a persons view to the top of a building for example. Or another example would be if a person is standing on a building that is a certain height and looking down at a object a certain distance away, what would be the angle of depression that they’re looking down. That example I believe uses more of the inverse aspect of trigonometric functions as you would set up all the variables and solve for the angle. As stated, in other instances you could have a height and a degree value and solve for the variable missing like distance. These are some examples of what comes to mind for me when I hear the phrase trigonometric inverse functions because it is both that and furthermore something to use in the real world. An example of people using inverse trigonometric functions would be builders such as construction workers, architects, and many others. An example of the use would be the creation of bike ramp. You will have to find the height and the length. Then find the angle by using the inverse of sine. Put the length over the height to find the angle. Architects would have to calculate the angle of a bridge and the supports when drawing outlines. These calculations are then applied to find the safest angle. The workers would then uses these calculations to build...

\( \newcommand\) • • • • • • • • • • • • • • • Use a calculator to find sine, cosine, and tangent in basic applications Work it Out 1 Two students, Manny and Julisa, were having a debate about the how to model the wavelength of their school's radio station frequency. To simplify their debate, they used another model of a wave as shown below. Figure \(\PageIndex\right)\) and Julisa says it is \(f(x)=5 \cos x\). • Without graphing the equations, can you tell which student is correct, and if so, who? • How do you know? • What would the graph of the incorrect equation look like when compared to the graph above? Discussion Recall that the equation for a cosine function is \(y=A\cos(w(x−h))+k\) where \(A\) changes the But is it a cosine function like Julisa believes, or a sine function with a shift in the phase like Manny believes? If you graph these two functions, and also \(y=5 \sin x\) you will see the subtle, but important differences between the three graphs. Work it Out 2 Figure \(\PageIndex\) The amplitude of the function of the co-height is 50 because the car will range between +50 and -50 feet away from a vertical line (like the \(y\)-axis) going through the center of the Ferris wheel. Therefore, the co-height can be represented by the function \(f(\theta )=50 \cos(\theta)\). Don't forget: you still need to create a graph and find the function for the height of Car 1. Example \(\PageIndex\) The above is a graph of the function \(Y(\theta )=50 \sin \theta +60\). Work it ...

One example of an inverse trigonometric function is the angle of depression and angle of elevation. I believe these two fit as a plausible example because they use sine or cosine or tangent in order to determine the angle of a persons view to the top of a building for example. Or another example would be if a person is standing on a building that is a certain height and looking down at a object a certain distance away, what would be the angle of depression that they’re looking down. That example I believe uses more of the inverse aspect of trigonometric functions as you would set up all the variables and solve for the angle. As stated, in other instances you could have a height and a degree value and solve for the variable missing like distance. These are some examples of what comes to mind for me when I hear the phrase trigonometric inverse functions because it is both that and furthermore something to use in the real world. An example of people using inverse trigonometric functions would be builders such as construction workers, architects, and many others. An example of the use would be the creation of bike ramp. You will have to find the height and the length. Then find the angle by using the inverse of sine. Put the length over the height to find the angle. Architects would have to calculate the angle of a bridge and the supports when drawing outlines. These calculations are then applied to find the safest angle. The workers would then uses these calculations to build...

\( \newcommand\) • • Focus Questions The following questions are meant to guide our study of the material in this section. After studying this section, we should understand the concepts motivated by these questions and be able to write precise, coherent answers to these questions. Let \(A, B, C\), and \(D\) be constants with \(B > 0\) and consider the graph of \(f(t) = A\sin(B(t - C)) + D\) or \(f(t) = A\cos(B(t - C)) + D\). • What does frequency mean? • How do we model periodic data accurately with a sinusoidal function? • What is a mathematical model? • Why is it reasonable to use a sinusoidal function to model periodic phenomena? In Section 2.2, we used the diagram in Figure \(\PageIndex\) is one-quarter of a period. In Progress Check 2.16, we will use some of these facts to help determine an equation that will model the volume of blood in a person’s heart as a function of time. A mathematical model is a function that describes some phenomenon. For objects that exhibit periodic behavior, a sinusoidal function can be used as a model since these functions are periodic. However, the concept of frequency is used in some applications of periodic phenomena instead of the period. Definition The frequency of a sinusoidal function is the number of periods (or cycles) per unit time. A typical unit for frequency is the hertz. One hertz (Hz) is one cycle per second. This unit is named after Heinrich Hertz (1857 – 1894). Since frequency is the number of cycles per unit time, and the...

By clicking “Submit,” you agree to receive recurring advertising emails, text messages and calls from Mathnasium and its independently owned learning centers about our offerings to the phone number/email provided above, including calls and texts placed using an automatic telephone dialing system. Consent to receive advertising text messages and calls is not required to purchase goods or services. By clicking “Submit,” you also consent to Mathnasium's Terms of Use and Privacy Policy. Trigonometry is a very different subject than most of the math we encounter in our lives previously, and it takes a different way of thinking to understand. For that reason, many people just want to get it over with when trig comes up in school. This article from enbibe (Source:https://www.embibe.com/exams/real-life-applications-of-trigonometry/ ) explains how useful trigonometry can be in a wide range of real-life applications! Trigonometry simply means calculations with triangles (that’s where the tri comes from). It is a study of relationships in mathematics involving lengths, heights and angles of different triangles. The field emerged during the 3rd century BC, from applications of geometry to astronomical studies. Trigonometry spreads its applications into various fields such as architects, surveyors, astronauts, physicists, engineers and even crime scene investigators. Now before going to the details of its applications, let’s answer a question have you ever wondered what field of scienc...