You finally made it through algebra, and the next step forward is a course in precalculus. While this is the logical path to take when learning math, a lot of students would rather skip right into calculus. This would be, for the most part, a huge mistake for students pursuing a math education. When it comes to courses in mathematics, you will find that the advanced courses depend heavily on a solid foundational understanding of concepts discussed in earlier courses. Avoiding precalculus can cause a student to be disadvantaged later in their math education. Here are a few reasons why.
Moving Forward Without the Trigonometry Component
Precalculus is typically where most students studying mathematics get their feet wet learning important concepts in the area of trigonometric functions. A lot of time is spent in the beginning sections of precalculus grounding a student in key trigonometric angles of the unit circle. Then students learn about functions like sine, cosine and tangent functions, just to name a few. A lot of time is spent graphing many of these functions, looking at arc-functions and using known information about triangles to determine the values of missing sides or angles. There is also a lot of information in a precalculus course aimed at working with key trigonometric identities. If you tried to skip over this foundation and jumped head first into calculus, you would find that you would be missing out on an important foundation when it comes to dealing with differentiation and integration of trigonometric functions you would virtually have no formal experience with using. You might want to reach out to a professional precalculus tutor near you to help increase your knowledge. You would also find that without a strong foundation in using trigonometric identities that you would not be able to get through a ton of calculus problems. Many calculus problems depend heavily on the ability to use trigonometric identities to manipulate these problems into a more manageable form. This becomes more intense by the time you get to the second semester of calculus. Consequently, you need the skills taught in precalculus to properly navigate through later courses in calculus. In other words, you are going to have to learn the information introduced in precalculus anyway if you want to continue forward with higher level math tutors. Similar problems would arise by the time you reached Differential Equations or Linear Algebra, because many of the core ideas from the trigonometry sections of precalculus are still being employed in these later courses as well.
Dealing with Parametric Functions and Beyond
Another amazingly important side of precalculus is that it covers a lot of information on parametric functions. It is here that you get to learn how to rewrite a system of functions in terms of a single variable to look at what it means to graph and employ these methods to solve real world problems. This foundation will prepare you for a third course in calculus where parameterized functions become an important part of studying the way parameterized vector functions behave. You also get to touch on an elegant idea called the de Moivre’s Theorem which states that (cos t + i sin t)^n = (cos nt + i sin nt) when n is an integer and t is a real number. You also get to learn about how e^it = (cos t + I sin t) can be used to develop an important relationship between complex functions and exponential functions. These are all ideas that are later developed more rigorously when you get to study Taylor Series Expansions in calculus and other courses like differential equations. So, as you can see, the concepts you learn in a course in precalculus prepare you to tackle much more difficult sections in other math courses you will be taking later.