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Trigonometric functions (sin, cos, tan, csc, sec, cot) relate the angles and sides of triangles. They extend to the unit circle for all angles and are fundamental in physics, engineering, navigation, signal processing, and wave analysis.

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1. 1In a right triangle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent
2. 2Mnemonic: SOH-CAH-TOA
3. 3Unit circle definition: sin θ = y-coordinate, cos θ = x-coordinate, at angle θ from positive x-axis
4. 4Reciprocals: csc = 1/sin, sec = 1/cos, cot = 1/tan

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