Interpreting Trigonometric Expressions in Stringology forms

From the definition of Geometrifying trigonometry we know as in previous post that

Combinatorial properties of Geometrifying trigonometry

Following these definitions if we interpret Sin(Θ) and Cos(Θ) then look picture below here Here HP means Hypotenuse is projected on Perpendicular which is H.P(dot is omited sometimes for convenience in wriing,HP means H.P)

HB means H.B

P*H is not multiplication of P to H.This means H of second (right side) HEA arrangement is scaled to fit and aligned to P of left side HEA arrangement

Similarly

B*H means H of right side triangle(subset of HEA arrangement) is scaled to fit and aligned with B of Left side(triangle which is subset of Left side HEA arrangement)

HEA Arrangement is well defined in previous post .It is Hipparchus Euclid Arrangement (HEA Arrangement)

This is the set HEA Arrangement which is fundamental basis set for Geometrifying Trigonometry

Zoomed the circle to see better

Geometrifying Trigonometry: namespace Tekla.CopyGADrawing

Concerns in Geometrifying Trigonometry and the Building Informations Modeling Issues

Concerns:Geometrifying Trigonometry:Overlapped Line segments Jungles

Geometrifying Trigonometry: public class TeklaDrawingAPIServices

Geometrifying Trigonometry

Geometrifying Trigonometry:[Cos(Θ)]^6 Representations

SanjoyNaths Conjecture:Geometrifying Trigonometry: Tips of Line Segment (1+(Sin(Θ))^2)^0.5 and (1+(Cos(Θ))^2)^0.5 forms Cyclic Quadrilateral

Corollary:Geometrifying Trigonometry: Cos(Θ) x Sin(Θ)=Sin(Θ) x Cos (Θ) has 25% Chance to become equal

Corollary:Geometrifying Trigonometry: Cosec(Θ) x Cosec(Θ) - Cot(Θ) x Cot(Θ) = 1 represents PHPH - PBPB=P

Corollary:Geometrifying Trigonometry:Sec(Θ) x Sec(Θ) - Tan(Θ) x Tan(Θ) =1 That means BHBH-BPBP=B (The initial line segment considered as 1)

Corollary:Geometrifying Trigonometry:Tan(Θ) x Tan (Θ) is not Tan Squared Theta but it is BP * BP

Corollary:Geometrifying Trigonometry: Cos(Θ) x Cos (Θ) is not Cos Squared Θ it is HB*HB the line segment

Corollary :Geometrifying Trigonometry:Sin(Θ) x Sin (Θ) is not Sin Squared Θ , It is HP*HP

Theorem 10: Geometrifying Trigonometry :There are 6 Types of Equality in Geometrifying Trigonometry.≡ , = , ≈ , Æ , æ and ₧

HEP Arrangement is a Locked Set

Theorem 9:Geometrifying Trigonometry :Need definition of 1 and 0 for eiπ+1=0 Which is defined here (The initial line segment considered as 1)

Theorem 8:Geometrifying Trigonometry: Number of defined Line segments in HEP Arrangement is rank of the System

Theorem 6 :Geometrifying Trigonometry:There are Two Fundamental Types of Trigonometric Expressions Simple and Compound

Theorem 3++:Geometrifying Trigonometry:Every of Predefined line segments Locked on Locked Set HEP Arrangement has two Trigonometric Ratios involved

Theorem 7:Geometrifying Trigonometry: Every Compound Douplet String of Geometrifying Trigonometry Does not mean Reciprocal of Given Expression.

Theorem 3+:Geometrifying Trigonometry:The Division of Trigonometric Expression means a Star(*) Operation in String Duplets

Theorem 3:Geometrifying Trigonometry:The Multiplication of Trigonometric Expressions means a Star(*) Operation in Strings Duplets

Theorem 1 : Geometrifying Trigonometry :Contiguity of Intermediate Dot Operation is Worthless Other than First and Last Alphabet

Theorem 2: Geometrifying Trigonometry:Reciprocal String (Duplet) for Simple Ratios under Dot Operation is Reverse of that String(Duplet)

Strings in Geometrifying Trigonometry and interpretations(Part 2 HEA or HEP)

Circles Fourier Series and Geometrifying trigonometry GT String Formal Systems

Strings in Geometrifying Trigonometry and interpretations(Part 1 with Dots and Stars)

Operators , Their actions and Interpretations on GT String

Interpretation of Pythagoras Theorem in Geometrifying Trigonometry HBHB+HPHP=H (Line segment H Itself )

37 Line Segments and 10 Points Identified to Symbol set of Geometrifying Trigonometric Formal System

Automated Symbolic formulation of operations and formations due to operations on GT Strings in Geometrifying Trigonometry

Implementation of First order ,Second Order And Higher Order logic through Stringology on Geometrifying Trigonometry

Some more stringology with Geometrifying of Trigonometry

Combinatorial properties of Geometrifying trigonometry

Geometrifying Trigonometry Fundamental rules explained

Some First words on Geometrifying trigonometry

Geometrifying Trigonometry