WHAT IS TRIGONOMETRY

WHAT IS TRIGONOMETRY

  • Trigonometry is a branch of Mathematics that studies triangles and the relationship between their sides and the angles.
  • The Word “ TRIGONOMETRY ” is derived from the Greek words ,  “ TRI ” (Meaning – Three),  “GON ”(Meaning – Sides), “METRON” (Meaning – Measure).

TRIGONOMETRY  = TRI + GON + METRON

INTRODUCTION TO TRIGONOMETRY

  • Let us consider a right triangle . Here angle A is an acute angle and the position of the side BC with respect to angle A. We will call the side Opposite to angle A.  AC is the Hypotenuse of the right triangle and the side AB is the part of angle A. So, we will call it as the side Adjacent to angle A                                                                         
WHAT IS TRIGONOMETRY
  • The Hypotenuse is the longest side, and is always opposite the right angle.
  • The Opposite side is the one opposite the angle we are interested in.
  • The Adjacent side is the one next to the angle we are interested in.

TRIGONOMETRIC RATIOS

  • This section presents the 3 basic Trigonometric Ratios  Sine, Cosine and Tangent.  The concept of similar Triangles and the Pythagorean Theorem can be used to develop the Trigonometry of right Triangles.
  • The Trigonometric ratios of an acute angle  in a right triangle ABC are defined as follows.
  • Sin A   =   Side Opposite to angle A/Hypotenuse = BC/AC 
  • Cos A   =   Side Adjacent to angle A/ Hypotenuse = AB/AC 
  • Tan A   =   Side Opposite to angle A/Side Adjacent to angle A = BC/AB 
  • Since hypotenuse is the longest side in a right triangle, therefore, the value of sin A or cos A is always less than or equal to 1.

Relationship between Trigonometrical Ratios

  • Cosec A   =  1/Sin A   = Hypotenuse/Side Opposite to angle A = AC/BC
  • Sec A   =  1/Cos A   = Hypotenuse/Side Adjacent to angle A = AC/AB
  • Cot A   =  1/Tan A   = Side Adjacent to angle A/Side Opposite to angle A = AB/BC
  • Tan A = Sin A/Cos A = BC/AB

Trigonometric Identities

An equation involving trigonometric ratios of an angle is called a trigonometric identity if it is true for all values of the angle.

For any acute angle A, we have

  1. Sin2A + cos2 A = 1
  2. 1 + tan2A  = sec2A
  3. 1 + cot2A  = cosec2A

NOTE:    Trigonometry is the study of triangles. Using trigonometry we can solve many problems precisely where we may have only been able to approximate before. Trigonometry is used in everything from Engineering and Architecture to G.P.S

Question.  In   triangle   ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Find the value of sin A and cos A.

What is trigonometry

Solution:                                                                           

By using the Pythagoras theorem, we have

                               AC2   =   AB +   BC2

                              AC2    = (24)2  + (7)2  

                              AC2   = 576   + 49 

                               AC   = √625  = 25 cm.

    .                        sin A = BC/AC   = 7/25 ,                   

                           cos A   = AB/AC   = 24/25                      

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