Super Hexagon To Learn All Trigonometry Formulae | Trigonometry Class 10
Building Magic Hexagon For Trigonometric Identities
Construct the hexagon and locate ‘I’ at the center of the hexagon.
Write tan on the farthest left vertex of the magic hexagon.
Use quotient identities ( tan x = sin x/cos x ) for the tangent going clockwise
Locate the “co” - functions such as cot (cotangent), csc (cosecant), and sec (secant) on the opposite vertex of the hexagon
To help you remember: all the “co” functions are placed on the right side of the hexagon.Along the outside edges of the hexagon, we can now follow around the clock (in either direction) to get the quotient identities. The quotient identities given below are in two equivalent forms of each.
Trigonometric Ratios:
The Three Main Trigonometric Ratios are:
sinθ=Opposite Side/Hypotenuse Side
cosθ=Adjacent Side/Hypotenuse Side
tanθ=Opposite Side/Adjacent Side
The Inverse of the Above Ratios are:
secθ=1/cosθ=Hypotenuse Side/Adjacent Side
cosecθ=1/sinθ=Hypotenuse Side/Opposite Side
cotθ=1/tanθ=Adjacent Side/Opposite Side
Below are the Relation between the Trigonometric Identities:
tanθ=sinθ/cosθ
cotθ=cosθ/sinθ
sin^2θ+cos^2θ=1
tan^2θ+1=sec^2θ
cot^2θ+1=cosec^2θ
sin2θ=2sinθcosθ
cos2θ=cos2θ−sin2θ
tan2θ=2tanθ1−tan2θ
cot2θ=cot2θ−12cotθ
First Quadrant
sin(90−θ)=cosθ
cos(90−θ)=sinθ
tan(90−θ)=cotθ
csc(90−θ)=secθ
sec(90−θ)=cscθ
cot(90−θ)=tanθ
Second Quadrant
sin(180−θ)=sinθ
cos(180−θ)=−cosθ
tan(180−θ)=−tanθ
csc(180−θ)=cscθ
sec(180−θ)=−secθ
cot(180−θ)=−cotθ
Third Quadrant
sin(180+θ)=−sinθ
cos(180+θ)=−cosθ
tan(180+θ)=tanθ
csc(180+θ)=−cscθ
sec(180+θ)=−secθ
cot(180+θ)=cotθ
Fourth Quadrant
sin(360−θ)=−sinθ
cos(360−θ)=cosθ
tan(360−θ)=−tanθ
csc(360−θ)=−cscθ
sec(360−θ)=secθ
cot(360−θ)=−cotθ
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Music:- Maestro Tlakaelel
Artist:- Jesse Gallagher
Attribution:- https://pngtree.com
Chapters:-
0:00 Introduction
0:19 Trigonometric Ratio
2:16 Trigonometric Identities
3:24 Complementary Angles or Formulae
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