Trigonometry is the study of triangles. It deals with the study and relationship of the lengths of the sides and the angles of a triangle. At the beginning of the 3rd century BC, trigonometry was evolved to study astronomical facts and figures. Columbus used trigonometry to calculate the circumference of the globe, using shadows and trigonometry. And he calculated it with just a 10 percent error!
As difficult as it may seem, trigonometry has practical applications everywhere. From home to astronomy, many people have used trigonometry and are continuing to do so.
Trigonometry is famous for confusing students with ratios and relationships. It may seem strange, but it is neither easy nor difficult than any other stream of math. It requires an understanding of concepts and also of the problem. Once you understand the problem statement, you will be surprised to see how useful these trigonometric identities are for you.
To break the taboos around trigonometry and help students gain confidence in the subject, we have listed a few techniques. This will help you understand the subject and perform well during your exams.
1. Use the Knowledge of Geometry
It is not difficult to decipher the utility of geometry in trigonometry. The study of triangles requires your concept of construction of triangles, too, especially right-angled triangles. Now let’s put our mind to work. The first thing that comes to our mind after hearing right-angled triangles is the Pythagoras theorem. In the earlier classes, we study that the sum of squares of the opposite sides is equal to the square of the hypotenuse. A simple geometric construction helps us to understand the theorem.
While we start studying trigonometry, the Pythagoras theorem plays a pivotal role in defining the course of our study. It is the starting point and is used throughout the course.
2. Memorize Certain Ratios
The first time we see trigonometry, we hear sin, cos, tan. Hence, begin your study from there. Understand what these words stand for.
Sin stands for sine of an angle in the right-angled triangle.
Cos stands for cosine of an angle in the right-angled triangle.
Tan stands for the tangent of the right-angled triangle.
These are the trigonometric ratios and constitute the basics of trigonometry help. One has to memorize the ratios they imply.
SOH, CAH, and TOA are words that will be very useful to you.
Sin(Θ) = Opposite / Hypotenuse [SOH]
Cos(Θ) = Adjacent / Hypotenuse [CAH]
Tan(Θ) = Opposite / Adjacent [TOA]
Let’s see an example,
Adjacent = 3 cms
Opposite = 4 cms
Hypotenuse = 5 cms
Sin(Θ) = Opposite / Hypotenuse = 4/5
Cos(Θ) = Adjacent / Hypotenuse = 3/5
Tan(Θ) = Opposite / Adjacent = 4/3
3. Memorizing Trigonometric Functions and their Correlations
Just like we have sine, cosine, and tan, we have cosecant, secant, and cotangent.
These are the inverses of sin, cos, and tan. Let us see their ratios with sides and correlations.
Cosecant or cosec = 1/sine = Hypotenuse / Opposite
Secant or sec = 1/ cosine = Hypotenuse / Adjacent
Cotangent or cot = 1/tangent = Adjacent / Opposite
Memorizing these six ratios make triangles one’s friend in the study of trigonometry. Once you memorize these, you can go ahead with numerical and advanced theories in the subject.
4. Have your Identity Toolbox
Trigonometry is full of identities, theorems, formulae, ratios, etc. As you move ahead in the course, you will find new identities now and then. Sometimes, it gets difficult to keep track of all the ratios and identities. Thus to prevent any confusion, you should keep a toolbox or a notebook where you can write all the important identities you encounter. These will help you at the end of the course when you deal with the applications of the concepts. Instead of switching back and forth among pages, you can refer to your toolbox and get all the data compiled.
These identities may seem daunting at first, but if you practice them thoroughly, you will understand them very easily. A formula book will thus help you to revisit those identities regularly. You can memorize them, use them, and master the problems of trigonometry.
Now that we have seen a few techniques to keep up with the study of trigonometry, we have for you a few don’ts as well. You need to keep yourself away from below mentioned things to keep yourself up with your studies.
The angle in trigonometry plays an important role in the subject. You need to pay attention to the unit of the angle. Units change a lot in the problems. The angle may either be given in degrees or radians. Make sure you know about the conversions and how to relate them with the trigonometric ratios.
2. Using radicals
While we deal with right-angled triangles, it is not always necessary to get a natural number while solving for the length of the sides. Hence make yourself comfortable with the radicals and decimals. They constitute most of the common mistakes done by students while solving trigonometric questions.
3. Use Correct Ratios
Some students get confused between the ratios and when to use them. Look for the information given in the problem statement. Use the information and manipulate it using identities to find the result. Write down every step to avoid mistakes and use of wrong identities.
We hope that this article will help you in planning for your next trigonometry test.
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