### In-Phase & Quadrature Sinusoidal Components

From the trig identity , we have*i.e.*, a relative phase shift of . It is also the case that every sum of an in-phase and quadrature component can be expressed as a single sinusoid at some amplitude and phase. The proof is obtained by working the previous derivation backwards. Figure 4.2 illustrates in-phase and quadrature components overlaid. Note that they only differ by a relative degree phase shift.

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Why Sinusoids are Important