The fundamental trigonometric identity derived from the Pythagorean theorem. Forms the basis for all other trig identities.
Unit circle — Any point on the unit circle has coordinates (cosθ, sinθ) satisfying x² + y² = 1.
Signal processing — Decomposing signals into sine and cosine components.
Physics oscillations — Simple harmonic motion: x = A×cos(ωt), v = -Aω×sin(ωt).
Navigation — GPS calculations use this identity for coordinate transformations.
Computer graphics — Rotation matrices rely on sin²+cos²=1 for length preservation.
Electrical engineering — AC current and voltage phase relationships.
Wave mechanics — Verifying wave function normalization.
Surveying — Calculating distances using angle measurements.
Astronomy — Converting between coordinate systems.
Architecture — Calculating roof angles and load distributions.
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