For A·sin(2πft + φ), the sine and cosine correlations are (A/2)cos φ and (A/2)sin φ, so 2√(⟨x,sin⟩² + ⟨x,cos⟩²) recovers A at every phase while either correlation alone passes through zero.
Sweep the amplitude and phase of a 5-cycle sinusoid; the two correlations trade off as the phase turns and the plotted pair travels a circle of radius A/2, while the recovered-amplitude readout holds constant.