Why is Trigonometry hard? (7 reasons with solutions to master this subject) - Maths How To with Anita (2024)

Trigonometry is one of the most challenging subjects for students to learn.

Many students find themselves struggling with the concepts and principles involved in trigonometry.

This can often lead to frustration and a feeling of being overwhelmed.

In order to help students overcome these challenges, it is important to understand why trigonometry is hard for many people.

As a high school math teacher since 2007 I have identified some reasons why students think trigonometry is hard and solutions to solve these problems and master this subject.

Trigonometry Terminology

One reason why trigonometry is difficult is that it involves a lot of new terminology. This can make it difficult for students to follow along in class and to complete assignments independently.

There are also similar abbreviations which can get quite confusing for some students. For example sec and cosec.

A possible solution to this is to create a trigonometry formula sheet and have it on your desk whilst completing homework. Use these tips to help you remember math formulas.

Non-linear: based on the circle

Additionally, trigonometry involves solving non-linear equations.

With right-angled triangles, there are only 3 types of equations to solve but in non-right-angled trigonometry, there are more complex problems using mathematical formulas.

On top of that Trigonometry is based on the unit circle with equations including r (radius) and θ(theta), the angle at the centre.

These problems can be difficult for students to understand without proper instruction and practice.

Some possible solutions to this is to pay attention in class, ask your teacher questions to clarify your understanding of each new concept, watch math Youtube videos to learn or ask an online math tutor.

Radians

Most students understand that angles are measured in degrees but throw in radians and this adds to the confusion.

Radians are another way to measure angles and they are represented by the greek letter π (pi).

There is a relationship between degrees and radians, which is: 360° = 2π radians.

This means that 1 degree is equal to π/180 radians.

Calculating the exact value of a trig ratio when it is given in radians often means one extra initial step of first converting to degrees which if done incorrectly can make the whole question wrong.

A solution to this is to learn some of the common conversions such as:

30° = π/6 radians

45° = π/4 radians

60° = π/3 radians.

90° = π/2 radians.

180° = π radians.

Memorization of exact values

The exact values of the trig ratios for angles of 0°, 30°, 45°, 60° and 90° must be memorized.

This can often lead to students feeling like they need to cram a lot of information into their heads which can be quite overwhelming.

Learning that they follow the pattern withn = 0, 1, …, 4for sine andn = 4, 3, …, 0for cosine makes it easier to recall them.

Coordinate geometry

Since the unit circle in Trigonometry is centered over a number plane, knowledge of coordinate geometry is helpful.

Especially for finding the values of boundary angles, 0°, 90°, 180°, 270° and 360°.

Recognizing and being able toplot points, lines and angles is a skill that needs to be developed.

Some solutions to this are attending geometry lectures, working on extra coordinate geometry questions at home, or joining a math club where you can practice with other students.

Trigonometric identities

There are a lot of trigonometric identities which can be used to solve equations.

However, students are often only taught a few of the basic ones and are expected to memorize them.

This can be quite daunting for some students and lead to frustration when trying to solve problems.

A solution is to add these to your Trigonometry formulae sheet and use them regularly to help you remember them. The Magic Hexagon is a clever resource for learning the trig identities and relationships. Print this out or draw one yourself on your Trig formula sheet.

Geometry and Algebra skills

Finally, trigonometry requires a strong foundation in algebra and geometry, which can be challenging for some students to develop.

Some trig questions are visual and students benefit from drawing the problem.

Others are more algebraic, requiring students to solve equations.

If a student is not confident in their algebra or geometry skills, this can make trigonometry quite difficult.

The solution here is to get extra help from a tutor or practice questions with a friend so that you can develop your skills in these areas.

Is Trigonometry harder than Calculus?

The short answer is no.

Calculus needs trigonometry to solve some problems.

Trigonometric functions are differentiated and integrated in Calculus in high school.

But it can be argued that trigonometry is more challenging than calculus because of the concepts listed above.

Some students find calculus easier because it builds on algebra which they have usually studied for a longer period of time.

Whereas, trigonometry is based on the circle, which can be confusing for some students.

Is Trigonometry hard compared to Algebra?

Again, the answer is no.

Algebra is a prerequisite for trigonometry, which means that algebra must be mastered before delving into trig.

But, once algebra is understood, trigonometry should not be overly difficult.

Some students find that mastering the concepts of angles and working with radians and degrees is the most challenging part of trigonometry.

But, with some practice, it is a manageable skill to learn.

Can I teach myself Trignometry?

Yes absolutely! By watching math videos on YouTube you can teach yourself Trig.

If you want to be successful, we recommend finding a study group or hiring a tutor to help you along the way.

It is important to have someone to bounce ideas off of and to help you understand the concepts if you get stuck.

But, it is possible to learn trigonometry on your own with some dedication and effort.

How is Trigonometry used in real life?

There are many applications for trigonometry in the real world.

Some of these include: predicting the movement of waves, mapping the surface of the earth, calculating distances between objects, and navigating aircraft.

Trigonometry is a fundamental tool that is used in many different fields. Bearings are used in Trigonometry in fields including navigation and surveying.

So, even if you don’t plan on using it in your career, it is still a valuable subject to study.

DISCLOSURE

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So is trigonometry hard?

Trigonometry is considered to be hard by some students. But with perseverance and the right mindset anyone can understand this subject and master it.

It is such a rewarding feeling every time you get a trig question correct.

We hope this article has helped you understand a little more about Trigonometry and whether it is hard or not.

Don’t forget to check out our other articles on Trigonometry for more tips and tricks!