What is trigonometric ratio and its importance.

Trigonometry is one of the principal branches in the history of mathematics and this concept is given by a Greek mathematician Hipparchus. Trigonometric functions are also acknowledged as a Circular Functions can be simply defined as the functions of an angle of a triangle. It indicates that the relationship between the angles and sides of a triangle are given by these trig functions.

Definition

Trigonometry is a study of the relationship of angles, lengths, and heights. It helps in finding the angles and missing sides of a triangle with the help of trigonometric ratios. The angles are either measured in radians or degrees. The commonly used trigonometry angles are 0°, 30°, 45°, 60° and 90°.

Trigonometric ratio

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

The three sides of the right triangle are: Hypotenuse (the longest side), Perpendicular (opposite side to the angle), Base (Adjacent side to the angle).

Six ratios

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Trigonometric Ratios

  • Sin θ = Opposite Side to θ/Hypotenuse
  • Cos θ=  Adjacent Side to θ/Hypotenuse
  • Tan θ = Opposite Side/Adjacent Side  & Sin θ/Cos θ
  • Cot θ=  Adjacent Side/Opposite Side  & 1/tan θ
  • Sec θ = Hypotenuse/Adjacent Side  & 1/cos θ
  • Cosec θ = Hypotenuse/Opposite Side  & 1/sin θ

Importance

Trigonometry has wide range of importance in subjects like astronomy and geography, developing computer music, chemistry number theory, medical imaging, electronics, electrical engineering, civil engineering, architecture, mechanical engineering, oceanography, seismology, phonetics, image compression and game development. The major applications of the concepts are given below

  • Estimating the heights of towers or big mountains
  • Determining the distance of the shore from the sea
  • Finding the distance between two celestial bodies
  • Determining the power output of solar cell panels at different inclinations
  • Representing different physical quantities such as mechanical waves, electromagnetic waves, etc.

 

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