Trigonometry studies relationships between angles and side lengths in triangles. It began with astronomy and navigation, where measuring angles was essential. The Greeks, Indians, and Islamic mathematicians developed early tables of sine and cosine.

The six trigonometric functions—sine, cosine, tangent, cosecant, secant, cotangent—relate angles to ratios. The unit circle extends these functions beyond right triangles to all angles. Identities like sin²θ + cos²θ = 1 connect them.

Trigonometry is used in physics, engineering, surveying, and computer graphics. It models waves, oscillations, and circular motion. Fourier analysis, which decomposes signals into sine and cosine components, is built on trigonometric foundations. The subject is both ancient and modern.

• Studies angles and triangle relationships
• Six trigonometric functions
• Unit circle extends to all angles
• Used in waves, physics, and graphics