Trigonometry is an integral part of mathematics that most of the students are scared of. It makes an important part of the career-related to engineering and architecture. Therefore, it is crucial to get an understanding of the topic well. It plays an important role in modern engineering, architecture, design, navigation, and many other related fields. Trigonometry is an easy and interesting subject. However, students find it hard. Let us understand what exactly is trigonometry and why students find it hard to understand. Moreover, you can learn trigonometry in a simple way through Cuemath.
What is Trigonometry?
As the name suggests, Trigonometry is all about the measurement of triangles. It gets made up of two words, ‘trigonon’ means triangle and ‘metron’ means to measure. Trigonometry studies the relation between angles and sides of triangles. Sine, Cos, and Tan are the main functions of trigonometry. It is the field of mathematics, which has many applications in real life. It is a very vast subject linked not only to geometry but also to different branches of maths, especially infinite series, logarithms, complex numbers, and calculus. The trigonometry field made an appearance in Greece for the first time in the third century. But many parts of it got lost, so it got redeveloped by Indian scholars.
Examples of Trigonometry
- Consider this example to understand the concept of trigonometry in simple terms. Suppose there is a sailboat, and you have to measure the height of the mast. Let us see this in the form of a triangle. If the mast is attached perpendicularly to the boat’s deck and the mast top is connected to the deck with rope, then rope, mast, and the deck together form the right-angled triangle. If we know the length of the rope from the mast and the angle between the deck and the rope, we can find the mast’s height using trigonometry.
- Let’s suppose we have the height of the building. Also, we know the angle formed when we see an object from the top of the building, then the distance between the bottom of the building and object is measured by tangent function, like angle’s tan is equal to the ratio of the distance and the height of the building.
Is Trigonometry Really Difficult?
Well, the answer is clearly no. Then why do students find it difficult? It is because they see the scope of trigonometry limited to their academics only. They are not able to relate it to real life, which makes them lose interest in the subject and finally makes them feel it hard to understand. Mathematics is one such subject through which many real-life problems can be understood and solved, and so is the case with Trigonometry. Basically, it’s a crucial subject, which has many real-life applications. There are mainly three functions in trigonometry, which are sine, cos, and tan. It is the core of trigonometry. If you understand this, then you can easily solve the problems of trigonometry.
Real-Life Examples of Trigonometry
To understand the concept well, and to relate it to real-life scenarios, consider the below examples:
- During the daytime, when the sun is out, the shadows of the objects are formed. The size of the shadows changes with time. As an example, the shadow is smaller during the daytime and gets longer in the evening. However, the size of the object is the same but the size of its shadow changes. The reason behind this is a change in the position of the sun with respect to earth, which can be relatable to trigonometry. It is because, as the sun changes its position, the angle of the sun rays with the earth also changes from 0 degrees to 180 degrees. That is why the shadow is not visible during the afternoon when the sun is just above the head, making a right angle with the earth. So when the angle changes from 0 to 90, the size of the shadow decreases. Similarly, when the angle changes from 90 to 180, the size of the shadow starts increasing again.
- Triangles make a crucial part of our life. This can be understood with another example. You must have seen the sliders in the park, where children slide from the slider. Now, if the angle of the slider gets changed, then will the children still be able to slide. It is an example of trigonometry, where the slider is designed considering the height, slope, distance, and other properties of the triangle.
- Talking about triangles, let us consider another important triangle in our lives. Have you ever wondered how triangles are used in the structure of a bridge? Here also trigonometry finds its application when bridges are designed. Again, different properties of the triangle, such as the length and angles between them are considered, so that these triangles can give full strength to the bridge above them.
- Now consider a painter who has to paint a wall. He will reach the wall with the help of a ladder while painting the middle and upper parts of the wall. Now he has to incline the ladder on the wall in such a way, the angle between the ladder and the surface is small to paint the lower and middle part of the wall. But, to paint the upper part of the wall, he has to increase the angle between the ladder and the surface to reach a higher level. It is again the concept of trigonometry. The painter knows how to align the ladder to reach a specific part of the wall and is unknowingly applying the concept of trigonometry.
How to Learn Trigonometry?
First of all, to learn Trigonometry, understand the right-angled triangle and different parts of a right-angled triangle such as base, perpendicular, and hypotenuse. The right-angled triangle is the triangle having one of the angles as 90 degrees. In the right-angled triangle, there is a base, the perpendicular, and the hypotenuse. Perpendicular makes a 90-degree angle with the base, and the hypotenuse is the side of the triangle, opposite to the right angle. Then understand the Pythagoras theorem, and after you go for the six ratios. Out of these six ratios, you have to understand the basic three ratios sine, cosine, and tangent. The remaining three ratios can be derivable from these three basic ratios.
As an example, Sin θ = Perpendicular / Hypotenuse
So, when we have to calculate the sine of the angle, then we need to look for the perpendicular and hypotenuse values.
Similarly, Cos θ = Adjacent / Hypotenuse
Tan θ = Perpendicular / Adjacent
Here, perpendicular, adjacent, and hypotenuse are parts of the right-angled triangle. Trigonometry is about the triangles and not just about the right-angled triangle, so learn the other ratios, i.e., Cotangent, Cosecant, and Secant.
Cot θ = Adjacent / Perpendicular
Csc θ = Hypotenuse / Perpendicular
Sec θ = Hypotenuse / Adjacent
As soon as you get comfortable with the six ratios of trigonometry, you can try to understand trigonometric ratios for different angles viz. 0, 30, 45, 60, and 90.
The unit circle is the special circle around which the whole trigonometry works. The Unit Circle has a center at 0 and has a radius of 1. This is because it is easy to find the sine, cosine, and tangent when the radius is 1. Also, it is denoted by the equation x2 + y2 = 1. Here, x2 is the Sin(x), and y2 is the Cos(x).
How to Make Trigonometry Easy?
In order to get a proper understanding of trigonometry, it is important to get the basic concept first. Once you understand, learn the step-by-step approach to solve the problems, and then you need to practice more and more problems. Try to practice different types of problems. The more you practice the problems, the more you will get a grasp on the topic. Once you get an understanding of the topic, solve the difficult problems. In this way, you will understand the concept and change your mindset from hard to easy.
Trigonometry is the study of triangles, angles, and other properties of the triangles. With trigonometry, you can understand and visualize the relations between the triangles. I hope now you have understood that trigonometry is not hard actually, and how you can relate it to real life. You can even learn trigonometry and get math exam tips from Cuemath. Similarly, you can learn the different concepts of maths and become a pro in the subject.