Angular Product Rule

Product Rule of Angles and Waves

All product events can be simplified to angular product, with amplification of a, as well.

(1)             A = ( (a ^ 1) * Sin ^ 1 ( θ [1] + Φ [1] ) )

* ( (a ^ 1) * Sin ^ 1 ( θ [2] + Φ [2] ) )

* ( (a ^ 1) * Sin ^ 1 ( θ [3] + Φ [3] )

* …

* ( ( a ^ n ) * Sin ^ 1 ( θ [n] + Φ [n] ) )

= ( a ^ n ) * Sin ^ n ( θ [1] + θ [2] + θ [3] + … + θ [n]

+ Φ [1] + Φ [2] + Φ [3] + … + Φ [n] )

(2) ( x * θ rad ) ^ n = ( x ^ n ) * θ rad,

(3) ( x * θ rad ) ^ n = ( θ ^ n ) * x m,

(4) ( 2 m * Pi rad ) ^ n = ( 2 m ^ n ) * θ rad,

(5) = 2 * θ rad ^ n m

When harmonic or relativistic angle, θ, is analysed by component, the result is that

c = critical, quantum

ω = 2 * n * Pi * f

= 2 * n * θ [c] * f [c]

= n * ( 2 * Pi rad * 1 Hz ), where the critical angular momentum is in parentheses

= n * ω [c]

All distances are interchangeable with angles, as ultimately they are all arcs or simply angles, as earlier stated.

© Xerqon Pty Ltd 2025

(first edition)

© Sydney Matinga 2026