TRIGONOMETRY: ACCURATE MEASUREMENT OF GEOMETRY

Whenever we hear the term ‘trigonometry’, the first thing that comes to our mind is only the right-angled triangle. However, the real use of trigonometry is not just limited to right-angled triangles. Trigonometry is a branch of mathematics primarily associated with the study of motion in two-dimensional and three-dimensional planes. Let’s understand it with a detailed explanation.

Whenever we study the motion of an object in a two-dimensional plane, we need its two components: the first is the horizontal component, and the second is the vertical component. These components are required to set various measurement parameters related to the object's motion. Along with these two components, we also need the slope of that motion. These two components are mainly two types of ratios: Sine and Cosine. Both ratios are taken along the horizontal and vertical axes with respect to the direction of the motion. With the help of these two ratios, many large calculations are done very easily. Projectile motion is a very common example of this.

Furthermore, trigonometry also plays a very important role in the study of ray optics and wave optics. In the case of complex numbers, Euler's rule also utilizes these two ratios, Sine and Cosine. It's just that there, the horizontal and vertical components transform into real and imaginary components. This makes it easier to formulate concepts related to wave propagation.

It is also very useful in many calculations related to alternating electric current, especially in determining phase-related parameters. The entire power transmission system depends on these parameters.

If we want to simplify calculations related to geometrical shapes, trigonometry is used there as well. Here, too, with the help of these two ratios, Sine and Cosine, many large calculations are performed. To achieve perfection in many innovative designs, very complicated calculations have to be performed. These calculations are made simplified with the help of Sine and Cosine ratios.

Now, if we talk about high-level applications, then creating architectural designs for large infrastructure without the help of trigonometry is impossible, and satellite launching or air traffic control systems, meaning navigation systems, are the best examples of the most advanced applications of trigonometry. When an airplane is in the air, and we want to know how high it is from a fixed point on the ground? Or when a ship or submarine is in the sea, then how far is it from a fixed point on land? Such calculations cannot be done without trigonometry.

Even in war, if a missile needs to be launched, the software used in the launching machines also employs the logic of trigonometry.

This is why trigonometry is a very interesting subject, and this interest can be increased with the help of good practice of trigonometry questions. That is why, on this website, you will find numerous practice questions related to every topic in mathematics, including trigonometry, with detailed explanations of solutions. Through these, people can become experts in mathematics. Additionally, these practice questions will be very useful for various competitive exams like IITJEE, GATE, CAT, GMAT, etc. So, find questions according to your topic and practice as much as you want.

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