# Do we really need Trigonometry?

### By Tracy Man

(Published on 8 October, 2021 )

Having been a secondary school Maths teacher for nearly a decade, I have had the opportunity to teach a wide range of students from various backgrounds, age groups, and abilities. However, when most students reach a certain age, they tend to ask the same set of questions:

• Why do I have to learn trigonometry?
• Is it useful?
• Who uses trigonometry in real life?

These are all great questions. But how would I, as a math teacher, reply? Well, apart from the typical textbook responses that it prepares you for college, you need it to get into a good college, or it teaches logical and critical thinking skills, Trigonometry, in fact, is a surprisingly common skill used by many people in a various fields and careers.

So, firstly, what is trigonometry? The word itself originates from the Greeks. “Tri” meaning triangle, “Gone” indicating the angles of polygons, and “Metron” is the art of measuring. Therefore ‘Tri-gono-metry’ can be translated as the art of measuring angle in triangles, or now more commonly known as the study of triangles, specifically its angles and dimensions.

Trigonometry has a long history. The first usages of Trigonometry dated back to as early as the Ancient Egyptians who used a more primitive form for building pyramids and Babylonian Astronomers utilised it to help keep detailed records on the rising and setting of stars. Sailors also had to rely on the stars to keep North when terrestrial landmarks were not available, meaning that the first known developers of Trigonometry were astronomers, sailors, and architects. In fact, Hipparchus, known as the Father of Trigonometry, developed trigonometry and constructed the first trigonometric tables during the 2nd century BC.

Hipparchus, Father of Trigonometry

Now, why, and how is this relevant to a 15-year-old student or to our everyday lives? Well, unlike mental arithmetic, Trigonometry may not actually have a direct impact on your daily life and cannot be applied to solve practical issues. However, look around you; from the building that you are currently standing in, to the mobile phone that has now become such an integral part of your life, all of these required the use of trigonometry in some way or form.

In terms of music, we know that sound travels in waves. Though the pattern of the waves is not completely the same, they strongly resemble a sine function. A Sine wave represents a single note, whereas multiple sine waves make a chord. Computers are not capable of listening to and understanding music as we do, therefore computers need to represent the waves mathematically to interpret music. Those who are interested in music theory or working in the music production, especially as sound engineers, should have at least some basic knowledge of trigonometry as knowing how to manipulate sine waves will help you create different and your desired sounds.

Apart from just keeping records of the stars like in ancient times, Astronomers use trigonometry to calculate the distance between stars and planets from Earth. NASA scientists also use trigonometry today when designing and launching space shuttles and rockets. Without a trigonometry, human beings would never have been able to travel to the moon and we would not have been ae to send any satellites into space.

Another field which uses extensively trigonometry and would probably be more relevant to our current generation, is gaming. Take the classic game of Mario for example, his movements are not just made in vertical or horizontal movements. In fact, when he jumps over objects, they are in the form of a parabolic curve. So, when writing the programs for games, trigonometry is used to represent how objects can move, and also for designing objects, characters, and sets.

Not just for calculating the height of buildings, we need trigonometry in construction to calculate the following:

• Measuring fields, lots and areas.
• Making walls parallel and perpendicular.
• Installing ceramic tiles.
• Roof inclination.
• The height of the building, the width length etc. and anywhere else that is necessary to use trigonometry.

Architects use trigonometry to calculate structural load, roof slopes, ground surfaces and many other aspects, including sun shading and light angles, all are important aspects to ensure that buildings are safely and properly constructed.

Other specialists and fields which also rely on trigonometry:

• In oceanography for calculating the height of tides in oceans.
• By marine biologists utilize mathematical models to measure and understand sea animals and their behaviour
• By marine engineers to build and navigate marine vessels.
• Calculus is made up of Trigonometry and Algebra.
• By physicists to calculate vectors and projectile motions
• By flight engineers in naval and aviation industries.
• In cartography (creation of maps).
• In criminology to calculate a projectile’s trajectory, to estimate the cause the of a collision in a car accident, calculate how and where an object fell from, or to identify the angle a bullet shot was shot from etc.

So, is it necessary for us to study trigonometry? Yes, it is one of the most important branches of Mathematics that you will learn in school. Not only is it a beautiful branch of mathematics, but it is also important to us. You as an individual may not directly use trigonometry, unless you decide to pursue a career or work in a field that utilizes it, but everything around us is reliant on the applications of trigonometry for it to function. And so, without trigonometry, we would struggle with our day-to-day lives.