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