Cosine-Sine Decomposition

This shows how a phase-shifted cosine can be decomposed into the sum of two components: a scaled cosine and a scaled sine. The red dashed line proves they sum to the original.

Formula: cos(t + Φ) = cos(Φ)cos(t) - sin(Φ)sin(t)

cos(t + Φ)

Complex Representation

e^(iΦ) = cos(Φ) + i·sin(Φ)

cos(Φ)cos(t)

-sin(Φ)sin(t)

π/4 ← Drag to see how the decomposition changes
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