Trigonometry is the branch of mathematics that deals with the relationships between side lengths and angles of triangles. Trigonometry has been around for thousands of years and has applications in several different fields from basic geometry to advanced calculus.
In this article, we will explore the difficulty of the various aspects of trigonometry to give you a better perspective of how hard trigonometry is.
Is Trigonometry Hard?
Trigonometry is a moderately hard branch of mathematics. The basic concepts in trigonometry are easy to understand. However, advanced topics in trigonometry such as trigonometric identities and Euler’s formula are much more difficult.
If you are reasonably capable in maths, you will not be particularly challenged by trigonometry. There are more difficult subject areas as far as mathematics is concerned. However, someone who has trouble understanding maths may find that trigonometry gets a little tough because of the functions involved and its non-linear nature.
One of the reasons why trigonometry gets confusing is that although it involves six main functions it evolves into further more complex functions. There are several derivations of formulae to convert these six main functions into many others.
Moreover, keeping track of all of these formulas is necessary to solve advanced trigonometric solutions. Oftentimes, you can only use a specific function for a given problem, and in case you are unable to recall it, you will be stuck.
Furthermore, trigonometry has a non-linear nature. All the calculations are based around a circle (no pun intended). For example, if you have Sin(π), you would expect Sin(3π/2) to have a greater value. However, that is not the case. This is a classical example of how trigonometry can be counterintuitive.
Someone who has a weak understanding of the way angles work and the impact of altering function values on the overall equation will find trigonometry unpleasant.
Another possible reason why trigonometry can become a little overwhelming is the use of radians to express angles. We have been using a degree system in our academic and daily lives.
Nonetheless, this is only a persistent problem for those who are generally not good with mathematics. Otherwise, after becoming familiar with trigonometry’s quirks, an average to a good student will be able to seamlessly navigate through the subject.
Even for students who do not believe their maths skills are up to par yet; consistent hard work and practice can make trigonometry much easier. It has its intricacies but generally, trigonometry is not an area of study that people find too challenging.
Is Trigomoetry Harder Than Calculus?
Calculus is harder than trigonometry because it is more advanced, complex, and challenging. Students also find calculus more difficult than trigonometry since there is no set way of approaching a problem.
This conclusion is derived from the simple fact that a good chunk of calculus requires you to understand trigonometric functions. Calculus is more advanced and therefore gives people a harder time.
With all the differentiation and integration going on in calculus, you end up with a large number of functions and rules to remember. Furthermore, calculus also requires you to understand the inner workings of logarithms, exponentials, and algebra.
In integration, for example, there is no set way to integrate a particular problem. You should be comfortable with all the methods to know which fits best in any particular scenario. This will undoubtedly take practice and hard work on your end. Therefore, calculus demands students to spend more time on it than trigonometry does.
Another reason why calculus is considered harder is that as you go along the road from trigonometry to calculus, concepts start getting more abstract and less grounded in everyday life.
Nonetheless, while calculus is difficult in its own right, regular practice will help in making the subject more bearable.
Is Trigonometry Harder Than Algebra?
If you find algebra difficult, any mathematics will pretty much be an impossible mountain for you to climb because all other subject areas use it to further solve their problems. That includes trigonometry. As such it can be deduced that trigonometry is harder than Algebra.
A lot of algebra revolves around linear equations, polynomials, and solving for unknowns. It is not comprised of too many complicated concepts and the problems are fairly straightforward once you have developed a good understanding of how to go about solving them.
In contrast, while not the hardest branch of mathematics, trigonometry still requires you to rack your brain more than algebra.
Moreover, people are more likely to encounter algebra in some form or the other in their daily lives. Although trigonometry has enabled us to make several advancements in the fields of science and technology, algebra is something everyone uses.
The repeated use of algebra in day-to-day activities makes it easier for people to understand it when they encounter it in their math classes.
Can I Teach Myself Trigonometry?
The short answer is yes, you can teach yourself trigonometry. Once you gain a solid concept of basic trigonometric functions, you can start solving problems to learn all the different ways a question can be approached and become comfortable with it.
Initially, you will have to have an understanding of algebra and geometry which are simple enough on their own.
After studying algebra and geometry you should be comfortable with angles, their relationship with the sides of different polygons, and how to find unknown values.
Next, you will have the sine, cosine, and tan functions of a triangle. From there on, you start building up how different functions are manipulated to fit your problem.
You can self-study by looking up videos online, watching recorded lectures by school teachers and college professors, and supplementing it by reading textbooks on the subject. Nowadays many online lectures can serve as substitutes for in-person classes.
Moreover, if you get stuck somewhere and cannot ask an instructor, you can always post your queries on any dedicated forum on the internet. You will easily get several replies and can even ask further questions to completely clear any confusion.
Next up, you need to practice your concepts.
This can also be done by going through problems in a textbook or exercises on the web. A lot of these have explanations along with answers to help you understand where you went wrong.
In summary, you have a vast number of resources at your disposal that will enable you to teach yourself trigonometry. Good luck!