To understand what is trigonometry, let us look at the following trigonometry examples:
1. Suppose a student goes to visit the Eiffel tower. If the student is looking at the top of the tower from a distance, then we can imagine a right triangle forming between the line of sight of the student, the tower and the base of the tower to a foot of student. Is it possible to find the height of the tower without actually measuring it?
2. A girl sees a hot air balloon in the air at a certain position A. After a while the balloon has moved to position B. Is it possible to find how high above the ground is the point B, considering that again there are right triangles formed between line of sight of the girl, the altitude of the balloons and horizontal distance between the girl and the balloons?
3. A boy is sitting on one bank of a river sees a bird on top of a tree on the other side of the river. Then a right triangle can be again imagined between, the line of sight of the boy, the width of the river and the height of the tree. Is it possible to find the height of the tree or the width of the river without actually measuring it?
For all the above examples, the distance or the heights can be calculated by using a special mathematical technique, which falls under a subtopic of math called “trigonometry”. The word ‘trigonometry’ if split to three parts: ‘tri’ (meaning ‘three’ in Greek), ‘gon'(meaning ‘sides’ in Greek) and ‘metron’ (meaning ‘measure’ in Greek). So we see that the word ‘trigonometry’ is derived from the Greek language. In math, trigonometry tells us how the angles and sides of a triangle are related.
In a right-angled triangle, for each of the acute angles, the ratio of the sides to each other are called trigonometric ratios of that particular acute angle. Though popularly the trigonometric ratios are studied for acute angles only, the knowledge of trigonometric ratios can be applied to other angles as well. The trigonometric ratios of a particular angle also obey some identities, which are called trigonometric identities.