Matinga's Cyclical Function Proofs

x = ω * t for a variable dimension, or for displacement evolution

h = ω * T for a constant dimension, dimensional interval, or for constant displacement or total displacement

Pythagoras Theorem

c ^ 2 = a ^2 + b ^ 2

Formula For Circle (Conic Sections)

r ^ 2 = x ^ 2 + y ^ 2

1 ^ 2 = x ^ 2 + y ^ 2 ,

Matinga Cyclical Functions

(1) y ^ 2 = a ^ 2 - x ^ 2 ,

(2) a * sin ^ 2 ( x )

(3) A = ( 1 - x ^ 2 ) ^ (1/2) ,

(4) sin ( x )

(5) A = cos ( x ) ,

(6) sin ( x + Pi/2 ) ,

(7) ( 1 - ( x - 1/4 ) ^ 2 ) ^ (1/2) ,

(8) cos ( x ) ,

(9) tan ( x ) = sin ( x ) / cos ( x )

(10) y ^ 2, A = x [1] ^ 2 + x [2] ^ 2 + x [3] ^ 2

+ . . . + x [n] ^ 2

The following example is an equation which describes a corkscrew effect

(11) A = ( ( a [ 1 ] ^ 2 - ( ( x - h [ 1 ] ) ^ 2 ) ^ ( 1/2 ) ) * ( arcsin ( a [ 2 ] * x + h [ 2 ] ) )

In (11) h = ω * T for 2 sets of dimensional intervals

Transpose powers and other operators as required. All circles add, and multiply to form further circles.

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