WHAT IS TRIGONOMETRY?

INTRODUCTION

In this chapter, we intend to study an important  branch of mathematics called '' TRIGONOMETRY''.

The word TRIGONOMETRY is derived from the Greek words: (i) trigonon and, (ii) metron. The word trigonon means a triangle and metron means measure. Hence, trigonometry means the science of measuring triangles.

TRIGONOMETRIC RATIOS AND ITS FORMULAS

  Ratios           Formulas

1. sinq = Perpendicular/Hypotenuse

2. cosineq = Base/Hypotenuse

3. tangentq = Perpendicular/Base                                                              

4. cosecantq = Hypotenuse/Perpendicular

5. secantq = Hypotenuse/Base                                               

6. cotangentq = Base/Perpendicular

 The perpendicular side is that the side which is front of the angle that we talk about.The hypotenuse side is the side front of right angle. and the remaining side is the base.

IDENTITIES

sin(θ) = 1/csc(θ)

cos(θ) = 1/sec(θ)

tan(θ) = 1/cot(θ)

csc(θ) = 1/sin(θ)

sec(θ) = 1/cos(θ)

cot(θ) = 1/tan(θ)

cot(θ) = cos(θ)/sin(θ)

                                       sin² θ + cos² θ = 1                              

                                              sin² θ = 1 − cos² θ                                   
                                              cos² θ = 1 − sin² θ                                   
                                              tan² θ + 1 = sec² θ                                   
                                              tan² θ = sec² θ − 1                                   
                                              cot² θ + 1 = csc² θ                                   
                                              cot² θ = csc² θ − 1                                   

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