R-Formulae

Introduction

The R-Formula, aka Harmonic Addition Theorem, is used to sum a Sine and a Cosine waves with varying amplitudes but with the same period. 

The formulas are as follows:

A sin θ ±  B cos θ = R sin (θ ± α)

A cos θ ±  B sin θ = R cos (θ ∓ α)

where R = √( A²  + B² ) is the new amplitude,

and α = arctan (B/A) is the phase shift ('+ α' is a rightward shift and '- α' is a leftward shift).