# What are trigonometric ratios and their importance?

Basically, trigonometry is a vast subject, and its concept was given by the Greek mathematician Hipparchus. Trigonometric deals with the measurement of angles and help us study the relationship between the sides and angles of a right-angled triangle. Generally, trigonometry starts by examining the right-angled triangles.

## Answer: The six trigonometric ratios are sine θ, cosine θ, tangent θ, cotangent θ, secant θ and cosecant θ. The importance of trigonometric ratios is that it is used in various places or in various subjects like civil engineering, mechanical engineering, medical imaging, electronics, electrical engineering, astronomy, game development, etc.

Let's understand trigonometric ratios properly with a few examples.

**Explanation:**

The relationship between the angles and the sides of a right-angled triangle with respect to any of its acute angles is expressed using trigonometric functions or trigonometric ratios.

The six trigonometric ratios are given as,

- Sin θ = Opposite Side / Hypotenuse
- Cos θ= Adjacent Side / Hypotenuse
- Tan θ = Opposite Side / Adjacent Side or Sin θ/Cos θ
- Cot θ= Adjacent Side / Opposite Side or 1/tan θ
- Sec θ = Hypotenuse / Adjacent Side or 1/cos θ
- Cosec θ = Hypotenuse / Opposite Side or 1/sin θ

The importance of trigonometric ratios is that it is used in various places or in various subjects like civil engineering, architecture, mechanical engineering, medical imaging, electronics, electrical engineering, astronomy, chemistry, geography, developing computer music, oceanography, seismology, phonetics, image compression, game development, etc. The major applications are given below.

- It helps in finding the heights of towers or any big mountains.
- It helps in getting the distance between two celestial bodies in the universe.
- It helps in getting the maximum power output of solar cell panels at different inclinations.
- It helps in finding the distance of the shore from the sea.
- It also represents different physical quantities like mechanical waves, electromagnetic waves, etc.