Most students find math to be a complex subject, and the two most important and most difficult topics are trigonometry and calculus. But which one is harder? It is a question I get asked by math students most of the time.
So, is trigonometry harder than calculus? Generally, most students find calculus harder and way more demanding than trigonometry because calculus requires using different theorems in problem-solving and involves a lot of effort. But calculus is beautiful, and most students enjoy studying it.
I also find that when it comes to math, the difficulty levels of any subject also depend on other factors, including the professor or teacher, the student’s skills, and their ability to work hard consistently.
Let’s take a look at some of the major differences between trigonometry and calculus so you can get an idea of which one is more challenging.
You might also enjoy reading: 9 Hardest Calculus Problems Ever You’ll Ever Encounter.
What Is Trigonometry?
Trigonometry means calculations with triangles. It studies relationships in mathematics involving lengths, heights, and angles of various triangles. It also includes studying angles and rotations in 2D and 3D space.
There are six functions of an angle typically used in trigonometry:
- Sine (sin)
- Cosine (cos)
- Tangent (tan)
- Cotangent (cot)
- Secant (sec)
- And cosecant (csc)
People use trigonometry in fields such as engineering, navigation, astronomy, physics, architecture, music theory, sports analysis, computer graphics, and more.
Trigonometry involves using formulas to solve problems or calculate angles or distances—including calculating the area of a triangle when given two sides and an angle—and requires a good understanding of algebraic concepts such as solving equations and working with functions.
It involves looking at relationships between right triangles and circles in order to solve problems related to them. Trigonometry requires knowledge of basic algebraic equations and functions in order to work out solutions to problems.
If you are a beginner in studying trigonometry, I encourage you to watch the video below to learn more about the basics of trigonometry.
What Is Calculus?
Calculus is another branch of mathematics that studies how things change over time. It looks at the rate at which something changes, for example, the speed at which something moves, and tries to calculate it using derivatives (the rate at which something changes) or integrals (the area under a curve).
Generally, people use calculus in fields such as physics, economics, biology, chemistry, medicine, engineering, finance, and computer science. Calculus involves finding limits (when something approaches infinity), taking derivatives (finding the slope of a curve), graphing functions (showing how one variable affects another), and integrating (summing up areas under curves), which requires an understanding of basic algebraic concepts such as exponents and logarithms.
It also involves understanding concepts such as limits, continuity, convergence, and divergence in order to solve complex equations.
To master calculus, you need knowledge about basic algebraic equations and advanced concepts like differential equations and vector analysis.
I encourage you to watch the video below introducing Calculus. And if you are looking for the best ways to learn Calculus online, I wrote a whole article sharing free online to help you Ace your calculus.
Should You Learn Trigonometry Or Calculus First?
It is generally recommended that you learn trigonometry first before calculus. Algebra, geometry, and trigonometry are typically prerequisites for Calculus. Each new topic in math builds on previous topics; learning trigonometry before Calculus will make studying Calculus less challenging.
Studying trigonometry will become easier when you know how to use Trigonometric rules and formulas.
To do well in Trigonometry, you need to make sure you have your trigonometric signs memorized. I also encourage you to remember the chain rule, the quotient rule, and the product rule.
I found mathematics fascinating; with a lot of practice, you will start to enjoy its brilliance by learning new tricks and approaches to solving complex problems.
Why Most Students Find Calculus Challenging?
I generally found that most students struggle with Calculus because they struggle with the algebra part of Calculus, not the calculus concepts themselves. If you find calculus hard, I recommend brushing up on algebraic manipulation before taking a calculus class.
If you are looking to quickly brush up on the most critical concepts before beginning calculus, I encourage you to start with Khan Academy’s free online resource.
Remember, Calculus deals with derivatives (the rate at which something changes) and integrals (the sum total over time). It examines how things change over time by looking at functions and their derivatives.
Why Do Students Find Trigonometry Difficult?
Most students find trigonometry difficult because it is a field of mathematics that is still abstract compared to other mathematical areas. In addition, many students usually find misconceptions, errors, and obstacles in learning trigonometry (Source: Journal of Physics: Conference Series)
What to read next:
- Is Linear Algebra Harder Than Calculus? (Yes, let’s find out why!)
- Are Differential Equations Harder Than Linear Algebra? (Find out now!)
- 9 Best YouTube Channels to Learn Calculus
- Is AP Calculus AB or BC Harder? (Let’s find out!)
Both Trigonometry and Calculus require knowledge of basic algebraic concepts. And they also both require dedication and practice to master.
Their difficulty level will generally depend on your level of mathematical knowledge and ability; if you have a strong grasp of basic algebraic equations, I believe trigonometry might be easier for you. And, if you are comfortable with advanced concepts like derivatives, then I think calculus might be easier for you.
I encourage you to review your prerequisites whenever you struggle with a subject. The truth is both Trigonometry and Calculus have unique challenges but don’t be too intimidated by either; just keep practicing and asking your professor questions until you grasp the required concepts.