Trigonometry
Class 10

Trigonometric Identity - Pythagorean

sin2θ+cos2θ=1\sin^2\theta + \cos^2\theta = 1
01234560.9999999999999999
sin²θ + cos²θ = 1

The fundamental trigonometric identity derived from the Pythagorean theorem. Forms the basis for all other trig identities.

Real-World Applications

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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