The discussion explores the relationship between the equations y(t) = A cos[ω(t)] + B sin[ω(t)] and C cos[ω(t) - σ], establishing that C = (A^2 + B^2)^(1/2) and tan(σ) = B/A. Participants clarify the expansion of C cos(ω(t) - σ) using the cosine angle subtraction formula, leading to a confirmation of the original equation. By defining A and B in terms of C and σ, they demonstrate that the two forms are equivalent. The relationship A^2 + B^2 = C^2 is reiterated, reinforcing the mathematical connection. This discussion effectively illustrates the trigonometric identities and their application in transforming sinusoidal functions.
