Trigonometry is the branch of mathematics studying relationships between angles and side lengths in triangles, particularly through functions like sine, cosine, and tangent. Born from practical needs in astronomy and surveying, it extends far beyond triangles—powering wave analysis, signal processing, physics, and engineering applications. The key mental model: angles as circular motion—every trigonometric concept traces back to points traveling around the unit circle, where position, rotation, and periodicity intertwine.

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