Trigonometry and precalculus are two courses that most math students take in high school. Trigonometry is generally taken during the sophomore or junior year of a student’s high school career, and precalculus is taken afterward or in the next year (the sequence varies between different schools). However, in some cases, students may have to choose between precalculus and trigonometry.
As a general rule, it is better to take precalculus instead of trigonometry since precalculus teaches the topics in trigonometry. Besides, precalculus covers most of the topics required to advance to calculus. Also, it has more application areas than trigonometry, which is specialized.
Are you a high school student who is going to choose the next step in math? If so, this article will help you make an informed decision. In this article, I will highlight why it may be better for you to take precalculus instead of trigonometry and give the answer as to whether you should skip trigonometry or not.
Precalculus vs. Trigonometry – Which Should You Take?
You should take precalculus, as it includes algebra, which is crucial for understanding calculus. Besides, unlike trigonometry, which is specialized, precalculus offers a solid grounding in algebra and trigonometry.
Generally, the goals of precalculus and trigonometry courses are similar. Notably, both aim to equip students with the necessary skills for handling rigorous concepts. However, there are some major differences, which brings us to the next point — why you should study precalculus.
Reasons To Take Precalculus
There are several reasons to pick precalculus instead of trigonometry. Generally, these reasons are closely linked to their differences.
Let’s look at them in detail.
1. Precalculus Includes Trigonometry
Precalculus is a course that enables students to study calculus in detail. It includes trigonometry, which prepares you for calculus. So when you’re looking at the bigger picture, it’s best to go for precalculus if you want to take on more challenging mathematics courses with ease.
2. Precalculus Has a Stronger Focus on Problem-Solving
Precalculus is focused more heavily on problem-solving, particularly with polynomial functions. Also, it typically involves learning about sequences, series, and complex numbers, which you won’t come across in trigonometry courses.
3. Precalculus Has a Stronger Focus on Understanding the Concepts
Precalculus allows students to gain a more in-depth understanding of mathematics. In some courses, you may be taught pre-and post-requisite skills simultaneously, such as when you’re taking a course focusing on function operations.
4. Precalculus Has a Wider Range of Applications
The skills taught in trigonometry are more likely to be applied when dealing with angles and triangles. Precalculus is also called “general” or “college” math for this reason, as it prepares students for calculus. It typically includes trigonometry content and provides a wide range of applications.
Here’s an excellent video that introduces precalculus:
In addition, many colleges have precalculus standards that students must meet before entering into calculus courses.
Tip: Before taking precalculus or trigonometry, I recommend consulting your school’s math department. This will enable you to choose the one that best suits their curriculum.
An Overview of the Topics Covered in Precalculus
The following list includes some of the topics covered in precalculus:
- Functions and their graphs: This may include basic algebra, functional notation, graphing equations, transformations of graphs, such as reflections, intercepts and asymptotes, concavity, end behavior, and domain/range.
- Sequences: This usually includes arithmetic sequences, geometric sequences, and arithmetic or geometric series.
- Series: This can include finite sums, infinite sums, explicit formulas for finite sums, Taylor Series, which includes power functions and polynomials, and Taylor polynomials, for approximating other functions.
To master these topics I recommend getting a copy of this Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry by Michael Sullivan (link to Amazon).
The author explains the ins and outs of the subject, starting with simpler concepts and building on them to more advanced ones. Also, it has chapter tests to ensure you master each concept before advancing to more complex ones.
Can I Skip Trigonometry?
You should not skip trigonometry. It is generally recommended that you take trigonometry before calculus. However, you might be able to move directly into precalculus if your school’s coursework allows. A precalculus course will cover all the topics in trigonometry.
Generally, most high schools and universities have a trigonometry prerequisite for their calculus courses. This means students may study trigonometry as a course or as a topic in their precalculus course.
Many students approach trigonometry with trepidation. The sheer mention of the course can cause anxiety. See Why Is Trigonometry So Darn Hard?
What Level of Math Is Trigonometry?
Trigonometry is a high school-level mathematics course. It provides students with the necessary skills for handling rigorous concepts in all areas of mathematics. Also, in some cases, trigonometry is a prerequisite to taking calculus.
That said, the specific levels of math may vary depending on the topic you’re studying. In this article, you can find a full rundown on what is considered “junior” and “senior” level math.
Tips on Passing Precalculus and Trigonometry
Whether you start with trigonometry or jump right into precalculus, there are a few tips you can follow to ensure success in your math courses.
Let’s take a look at these tips now.
- Write Down Every Step of the Process When Solving a Problem
A simple but often forgotten tip that will help you succeed is to write everything down. When learning new concepts, it’s helpful to take detailed notes. This will enable you to know what you’ve covered and what you still need to learn.
- Keep Up With Your Homework
It’s always beneficial to keep up with your homework assignments and study for tests or quizzes. This will help you focus on what you’ve learned in class and review any information similar to other topics covered in the past.
- Understand the Difference Between Memorizing and Understanding
There’s a big difference between memorizing something and understanding what you’re learning. If you find yourself stuck on any problems or concepts, ask your teacher for help. Often this leads to better results than just trying to solve the problem without any guidance.
- Don’t Be Afraid To Ask Questions
As mentioned, asking questions for help with problems is an excellent way to learn.
However, if you’re still stumped on any topics, don’t be afraid to ask your instructor or another student taking the course for help. You’d be surprised to discover that some of your classmates can explain those concepts in the simplest ways.
Ultimately, whether it’s better to take trigonometry or precalculus is a decision you’ll have to make with your school counselor. If your high school offers both courses and there’s room in your schedule for both, consider starting with precalculus. This will give you a solid foundation in the basics of mathematics that can be very helpful in later math courses.
Besides, precalculus courses include trigonometry. Because of that, if you take precalculus, you’ll already be familiar with trigonometry concepts by the time you complete the course.