What Is Trigonometry?

Trigonometry is one type of mathematics that specifically studies the relationships between angles and sides of triangular shapes. Trigonometry is used in geometry since every shape that has straight sides can be split up into a group of triangles. This branch of math explores the incredibly intricate relationships between itself and other types of math. From complex number systems to logarithms to calculus, trigonometry is used pretty much everywhere in mathematics. To put it simply, trigonometry is used to help one discover angles and distances in fields like science, mathematics, engineering, and more.

Trigonometry was first developed in Ancient Greece around 300 B.C. Many of the most important functions within trigonometry, such as the sine concept, was contributed by mathematicians and astronomers in India around 500 A.D.

Trigonometry is used in a variety of real-life applications. While it is rarely used for everyday practical uses, trigonometry is used in a wide range of industries. It is used in the development of electronic music, architecture planning, everyday flight planning for the aviation industry, determining the distance between planetary objects in astronomy, and in the investigation of crimes scenes in the criminology field.

Subdisciplines of Trigonometry

  • Pre-trigonometry (can include Algebra)
  • Elementary trigonometry
  • Plane trigonometry
  • Spherical trigonometry
  • Analytic trigonometry
trigonometry right-angled orthogonal triangle

How to Approach Learning Trigonometry

The right-angled triangle is at the core of trigonometry, as it serves as the basis for students to understand adjacent angles, opposite angles, and the hypotenuse. By understanding how to calculate the relation between the two sides at a 90-degree angle, we can discover the hypotenuse, or distance, from one side to the other.

Let’s consider a real-world example to get a better grip on what trigonometry helps us do. Let’s say you need to know the height of a building and the distance between the foot of a ladder to the top of that building to determine how long of a ladder you will need. In trigonometry, all you need to do is measure the height of the building and the distance from the foot of your ladder to the bottom of the building. Using the Pythagorean Theorem, you can find the distance or hypotenuse using this formula:

a^2 + b^2 = c^2
10^2 + 13^2 = c^2
c = 16.4 foot ladder is needed.

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Trigonometry Student Curriculum FAQs

High school trigonometry is quite basic and focuses on laying down the core concepts of trigonometry. This is done to give students a solid foundation of trigonometry concepts before moving on to complex classes in college or university. In general, the following is taught in high school trigonometry at most schools:

  • The Six Trigonometric Functions.
  • Circular Functions.
  • Graphs of Trigonometric Functions.
  • The Law of Sines and Cosines.
  • Using a graphic calculator.
  • Trigonometric Identities.
  • Trigonometric Equations.
  • The Polar Coordinate System.
  • Understanding graphs, points, and subsequent functions.
  • The use of trigonometry in the real world.

College trigonometry involves more complex concepts than high school trigonometry. Specifically, the first and second years of college are dedicated to reviewing high school trigonometry functions in addition to more complex functions, graphs, inverse functions, and unique identities. A few common topics taught in college trigonometry include complex trigonometric equations, triangle solutions, the form of complex numbers, polar coordinates, and their context in a variety of fields. Such fields include science, technology, and STEM industries. Students will need to take a math assessment upon entering college to determine if they are ready for college trigonometry. Most schools will accept adequate ACT and SAT scores to place students as well.

Many of the advanced trigonometry courses taught in third and fourth-year curriculums at universities will vary quite a bit. For the most part, students will learn advanced trigonometry via pre-calculus courses. Other advanced math courses taught at universities will include many different complex trigonometric concepts. Some common topics and concepts taught in advanced trigonometry include the following:

  • Analyzing functions using varying representations.
  • Interpretation and application of very complex numbers.
  • Building functions that replicate relationships.
  • Identifying trigonometric functions through the use of the unit circle.
  • Identification and application of advanced and complex trigonometric identities.
  • Performance of model vector quantities.

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How Do I Become a Trigonometry Tutor?

If you have a passion for teaching others and love trigonometry, becoming a trigonometry tutor is easy. You need a minimum of a high school degree or GED to start teaching kindergarten and middle school grade levels. You may need a degree in a specialist subject for higher-level trigonometry courses depending on the level of practice you plan to teach. The costs of trigonometry tutors vary because you will set your pay rates and time schedules depending on your own experience and circumstances.

Your first step will be to decide which topics you’d like to tutor. Then choose the age groups and grade levels you want to teach. Learn the curriculum and critical concepts for those grade levels. And lastly, establish your teaching methods, tools, and eventually, you will create your own course materials over time as you get more experience working with students.

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