In this article, we’re going to put trigonometry vs calculus in the battle and see what is the difference between these two mathematics topics.
Also, discover which is the hardest subject trigonometry or calculus?
So keep reading to prevent falling into some mistakes many students fall into.
Trigonometry vs calculus?
Trigonometry is a domain that studies triangles and all their aspects, it is a narrowed topic, unlike calculus where it is used in many areas such as algebra, geometry, and even trigonometry. So calculus is a broad and more complex domain than trigonometry.
what do students study in trigonometry?
3 important subjects students study or learn in trigonometry are:
- studying different forms of triangles
- learn how to represent a triangle in a circle
- learn how to use triangle functions to solve issues
step1: studying different forms of triangles
In the beginning, students learn and discover what is a triangle, and learn what are the angles. In general, triangles are divided into 3 categories.
- normal triangles
- Isosceles triangle
- equilateral triangle
so in the beginning students learn how to differentiate between these triangles and learn what it is the characteristics of every one.
later they learn the notion of angles that triangles have and how to calculate the angles of triangles based on some rules like Pythagoras‘ or some functions like Cosinus and Sinus. Also, measure the size or distance of ribs.
step 2: representing triangles in circles
The most important step to learn in trigonometry is angles and their relations to trigonometric functions. That being said you will learn how to represent trigonometry functions and angles.
This technic is helpful, helping you to determine angles and famous trigonometric relations between cos and sin. In addition, you will implement theses knowledge in calculus like determining the derivative of cos or sin function without needing to memorize them.
this is an image example that relates between circles and triangles.
Step 3: learn how to use the trigonometry rules like cos and sin
in trigonometry there are 3 principal functions that we use that are:
if you ask between trigonometry and calculus you should normally be aware. But in this step students go a little bit further and learn the application of these functions.
This step is a little hard and requires some effort of memorization and algebra to understand. Because they include these functions in equations to solve issues like in the example below.
In general, trigonometry is an easy subject compared to what we’re going to discover in the next paraph, talking about calculus.
what do students study in calculus?
The 3 principals components of calculus are:
step1 learning limits
A limit function is a mathematical tool that helps us understand how a particular equation behaves as we approach a certain value. This function can be used to calculate the slope of a line or the size of a curve at any given point. It’s helpful for figuring out things like how much water will flow through a pipe over time, or how much voltage is needed to make an electronic component work properly.
This can be helpful in finding max and min points on a curve. It can also be used with other functions to find when a function is defined or undefined. So, when we want to know the max or min of a curve, we use limits. For example, we can use a limit to determine how much the water will flow in a swimming pool.
normally limits are functions written in this form below:
step 2 derivative
Derivatives are a way of measuring how a particular number changes over time.
For example, if you have a car and you want to know how much it is worth now compared to when you first bought it, you would use derivatives.
Another example would be if you have a graph that shows how many oranges were sold each day over the course of a month. You could use derivatives to measure how the number of oranges sold changed from day to a day.
if you want to know more about derivatives you can read this article:
step 3 integral
Integral calculus is a field of mathematics that deals with the accumulation of quantities. It is used to find areas, volumes, and other measures of regions in space. For instance, calculating the area of a wing or a volume of a tank. Sometimes with complex shapes engineers can calculate a specific area like the image example below. So in this case, tend to use integrals.
The principle behind integrals is a mathematical function that split any shapes into small parts so engineers can measure the volume or areas of each part and then add them together to get a final measure or a given complex shape.
for further information about integrals, you can watch this video.
Difference between trigonometry and calculus?
trigonometry is a science that studies triangles including angles and rings, in other words in trigonometry you will deal with all mathematics relations that explain triangles. While calculus is a broad domain it includes many areas like algebra and even trigonometry itself.
to explain more, to study calculus you need to learn about trigonometry functions like cos and sin. In other words, you will include these functions to do many calculus calculations like:
- calculate a limited of cos or sin function
- make a derivative of the cos and sin function
- find an integral of cos and sin functions
So trigonometry must be the first step, for this reason, students study it in middle school, then study calculus later in high school and college. This order is important because math is a subject that is sequential.
you could read this article 4 important steps to learn math from the ground up
Which is harder than calculus or trigonometry?
Trigonometry is nothing to compare to calculus, calculus is considered the tough math subject in mathematics. To put you in the perspective, trigonometry is like the ABC of English. trigonometry is not complex such calculus. So there is nothing to compare between these 2 fields.
trigonometry is a field study only the science of triangles while calculus can be used in any area you might think about even in trigonometry itself.
Trigonometry and calculus are both important but in the beginning, you should learn trigonometry well and then go to calculus.
Having a weak foundation in trigonometry might provoke to you some problems in the future, especially the time when you are required to combine calculus and trigonometry as we mentioned in our article.