Introduction to Trigonometry

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In Mathematics, trigonometry is a branch that deals with the study of the relationship between the sides and the angles of a right-angled triangle. The main purpose of trigonometry is to find the unknown angle and the missing sides with the help of trigonometric ratios. Here, let us have a look at the six important trigonometric functions and also their inverse functions.

Six Important Trig Functions

In trigonometry, there are six trig functions. Among the six trig functions, the three basic functions are Sine (Sin), Cosine (Cos), and Tangent (Tan). From these three functions, the other three functions are derived such as Cosecant (Csc), Secant (Sec) and Cotangent (Cot), which are the reciprocal of Sine, Cosine, and Tangent functions, respectively. The ratios for these functions are basically derived from the sides of a right-angle triangle. The three sides are:

Hypotenuse Side – The longest side of a right triangle

Adjacent Side – The side next to the angle θ

Opposite Side – The side opposite the angle θ

 

Using the sides of the right triangle and angle θ, the six functions are given as follows:

  • Sin θ = Opposite side / Hypotenuse
  • Cos θ = Adjacent side / Hypotenuse
  • Tan θ = Opposite side / Adjacent side
  • Cosec θ = Hypotenuse / Opposite side
  • Sec θ = Hypotenuse / Adjacent side
  • Cot θ = Adjacent side / Opposite side

 

The inverse function of the trig functions is called inverse trigonometric functions. It is used to obtain the angle measure from any of the trigonometric ratios. It is also known as “Arc Functions”. It is a function defined in a certain interval. It means that the function is defined under the restricted domain with the specified range. We know that there are six trig functions. For all the six functions, there is an inverse function. Hence, the six arc functions are:

 

  • Inverse Sine (Arcsine)
  • Inverse Cosine (Arccosine)
  • Inverse Tangent (Arctangent)
  • Inverse Cosecant (Arccosecant)
  • Inverse Secant (Arcsecant)
  • Inverse Cotangent (Arccotangent)

 

Since trigonometry deals with the calculations of lengths, heights, and angles of a triangle, it has enormous uses in our daily life activities. Some of the applications are:

  • Measuring the height of a building
  • Used in the creation of maps
  • Used in Criminology, Marine Biology, Navigation and so on
  • Used in Satellite Systems
 

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