### In-Phase & Quadrature Sinusoidal Components

From the trig identity , we have

From this we may conclude that every sinusoid can be expressed as the sum
of a sine function (phase zero) and a cosine function (phase ). If
the sine part is called the ``in-phase'' component, the cosine part can be
called the ``phase-quadrature'' component. In general, ``phase
quadrature'' means ``90 degrees out of phase,'' *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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Sinusoids at the Same Frequency

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Why Sinusoids are Important