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Trigonometry

Trigonometry is the domain of mathematics that revolves around the connection between the angles and sides of a right-angled triangle. The word Trigonometry is made up of ‘Trigonon,’ meaning triangle, and ‘Metron,’ meaning measure. Trigonometry is majorly about right-angled triangles, where one internal angle is 90 degrees. Through it, you understand how to determine missing lengths of the sides or angles in a right-angle triangle.

The Basic Functions in Trigonometry

To understand this subject, you must be fully familiar with its basics. These deal with problems related to angles and their measurements. There are three primary functions.

  • Sin
  • Cosine
  • Tangent

Using these functions, you can decipher other functions, such as Secant, Cotangent, and Cosecant. To understand trigonometric concepts, you should know about these functions and their formulas.

Let’s start with the sides of a right-angled triangle. This triangle has the following sides:

  • Perpendicular – This is the side directly opposite to the angle θ.
  • Base – It’s the side adjacent to the angle θ.
  • Hypotenuse – . This side lies opposite to the right angle.

The Formulas of Trigonometric Functions

If you want to learn Trigonometry deeply, you must learn about the formulas of the basic functions. Trigonometric formulas demonstrate the relations between Trigonometric ratios and the angles for various quadrants.

Suppose a right-angled triangle has θ as the angle. In this case

  • Sin θ equals perpendicular/hypotenuse.
  • Tan θ equals perpendicular/base.
  • Cos θ equals base/hypotenuse.

The functions sec, cot, and cosec depend on cos, tan, and sin, respectively. So,

  • cot θ equals 1/tan θ

  • cosec θ equals 1/sin θ

  • sec θ equals 1/cos θ

Now, we can calculate cot θ, sec θ, and cosec θ functions with the following formulas.

  • Cot θ equals base/perpendicular.

  • Sec θ equals hypotenuse/base.

  • Cosec θ equals hypotenuse/perpendicular.

Angles in Trigonometry

The most commonly used angles in trigonometric problems are 90 degrees, 60 degrees, 45 degrees, 30 degrees, and 0 degrees. Besides these, other important angles are 360 degrees, 270 degrees, and 180 degrees. To determine these angles, you need to create a right-angled triangle. Here, one acute angle is the corresponding Trigonometry angle. The angles are specific to the ratios or functions related to it.

  • θ equals sin-1, which is perpendicular/hypotenuse

  • θ equals cos-1, which is base/hypotenuse

  • θ equals tan-1, which is perpendicular/base

Trigonometry is a crucial mathematical relationship. It’s all about triangles, which are one of the simplest forms. However, their mathematics is of much significance, particularly where there’s a need to determine precise distance measurements.

References:

Skills you need: Introduction of Trigonometry

Cue math: Trigonometry

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