Trigonometry is the field of mathematics that analyzes the ratio between triangles, angles, and lengths. Its concepts have assisted ancient explorers in tracking the stars and navigating the oceans, and real-life applications of trigonometry are now found everywhere. While you may think trigonometry is rarely used outside of the classroom, you will be amazed at how many instances and applications of trigonometry can be found in everyday life. Before we dive into the real-world applications of trigonometry, let’s ensure that you understand the basics of trigonometry. 

In school, you may have learned that trigonometry combines two Greek words, ‘TRIGONO,’ which means triangle, and ‘METRY,’ which means measure.

The History of Trigonometry

Triangles were first studied in Egyptian and Babylonian mathematics in the second millennium BC. They were also used extensively in Kushite mathematics. The systematic study of trigonometric functions originated in Hellenistic mathematics and made its way to India as Hellenistic astronomy. The study of trigonometric functions thrived in Indian astronomy throughout the Gupta period, thanks to Aryabhata, who developed the sine function.

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Trigonometry was a significant topic of study in Islamic mathematics during the Middle Ages, as demonstrated by mathematicians such as Al-Khwarizmi and Abu al-Wafa. In the Islamic world, where all six trigonometric functions were recognized, it became a distinct discipline. Beginning with Regiomontanus in the Renaissance, translations of Arabic and Greek writings led to trigonometry being recognized as a discipline in the Latin West. Modern trigonometry evolved during the Western Age of Enlightenment, beginning with 17th-century mathematics (Isaac Newton and James Stirling) and culminating with Leonhard Euler (1748).

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Modern Trigonometry

Modern trigonometry is heavily influenced by Babylonian, Sumerian, Greek, and Indian astronomers. Astronomy transitioned from a qualitative observational science to a predictive quantitative science with the discovery of trigonometry. This transformation popularized the applications of trigonometry by demonstrating that a mathematical representation of natural occurrences is feasible. Observational data might be translated into mathematical models for the first time. In this way, Ptolemy’s Almagest was a watershed moment, serving practical mathematics as Euclid’s Elements did for theoretical mathematics. 

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Concepts and Examples of Trigonometry

At its core, trigonometry refers to the measurement of a triangle. As you may know, a triangle comprises six parts: three angles and three sides. Their names and acronyms are:

  • Sine (sin)
  • Cosine (cos)
  • Tangent (tan)
  • Cotangent (cot)
  • Secant (sec)
  • Cosecant (CSC)

The fundamental notions of trigonometry are the angle functions and their applications to computations. So, the triangle measurement is the sum of its sides and angles. It helps in determining the angles and distances between structures, and focuses on right-angled triangles, i.e. triangles including one angle that is 90 degrees. 

Categories of Trigonometry

There are two categories of trigonometry that help understand how you can apply the concepts to real life. The ratio of the sides of a right triangle to their angles is the subject of core trigonometry.

  • Plane trigonometry is used to compute the angles of a plane triangle.
  • On the other hand, spherical trigonometry is used to calculate the angles of triangles drawn on a sphere.

Real Life Application of Trigonometry

Now, we will explore the historical uses of trigonometry and the different real-life applications of trigonometry.

A mechanical structure, such as a bridge or a building, is a simple example of trigonometry. An architect’s blueprint includes many trigonometric elements where their findings are compared for implementation into the plan. 

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Astronomy

Humans have been drawn to the mysteries of the solar system since the beginning of civilization. Throughout history, astronomers have used trigonometry to calculate the distances of stars and planets from Earth. Today, NASA scientists use it to construct and launch space shuttles and rockets. Humans would never have made it to the moon without trigonometry. 

Sound Waves

Trigonometry is also essential in musical theory and production. Sound waves move in a repeating wave pattern that can be visually represented by sine and cosine functions. A sine curve may represent a single note, and many sine curves can be used in combination to model a chord. A graphical representation of music enables computers to generate and comprehend sounds. It also allows sound engineers to view sound waves, altering volume, pitch, and other factors to get the desired sound effects. 

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Navigation

The control and monitorization of moving vehicles are explored in various forms of navigation. 

These forms include: 

  • Maritime navigation
  • Aviation navigation
  • Space navigation
  • Terrestrial navigation

The study of moving objects is known as navigation, and the angle or distance measured at that time is done with trigonometry. Compass, pinpoint poles, trigonometric ratios, and various formulas are utilized to determine the exact location of a moving body.

Trigonometry

Marine Biology

Marine biologists study marine life such as plants, animals, and other species that reside in the ocean. Trigonometry is utilized in marine biology to anticipate how far and at what angle a creature or plant is from the scientist. The angle might be a depression angle or an elevation angle, depending on where the observer is. The water level is regarded as the base of the right-angled triangle, while the item’s depth is considered to be the height slant distance. 

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Aviation

While a plane is flying, the wind plays an integral part in integrating safety and technology. Two perpendicular sides of a right-angled triangle depict the wind’s direction. So, we can compute the plane’s distance to its destination by applying the definition of trigonometric ratios. 

Industry of Manufacturing

Trigonometry is used extensively in the manufacturing industry, allowing producers to make everything from vehicles to zigzag scissors. Engineers use trigonometric relationships to predict the sizes and angles of mechanical parts used in machinery, tools, and equipment. This is vital in automobile engineering because it allows vehicle producers to accurately size each item and ensure that they operate together safely. 

Seamstresses also use it to determine the angle of darts or the length of cloth required to create a specific shape of a skirt or blouse.

Crime Investigation

Forensic scientists and crime detectives employ trigonometry functions to deduce what happened at a crime scene, study blood spatter, analyze gunshot holes to establish the angle of impact, and use navigation technology to pinpoint a criminal’s position.

Medical Imaging & Pharmacy

In orthopedics, trigonometry determines the degree of distortion of a vertebra and whether the nerves are injured. It is also used to shape prosthetic arms and legs as proportions are customized to facilitate operation at maximum potential function. Likewise, the diagnosis and treatment of illnesses using a variety of imaging, ultrasound, nuclear medicine, and magnetic resonance techniques are uses of trigonometry. They also utilize it to calculate the exact angles, allowing each beam to target the malignant cells precisely. Diagnostic radiology enables doctors to observe structures within your body.

A few more examples of where trigonometry techniques are widely applied are optics, statistics, electrical engineering, mechanical engineering, computer graphics, game development, civil engineering, cartography (creating maps), and crystallography (the study of atom arrangements in a crystalline solid).
At BYJU’S FutureSchool, students are offered an extensive curriculum to help master the concepts of trigonometry and overcome math anxiety. This specially designed coursework can give you the confidence to solve any math problem that comes your way. Sign up for FREE trial class in a 1:1 environment with a dedicated instructor to check it out.

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