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Arcs, or inverse trigonometric functions, are the inverse functions of the basic trigonometric functions sine, cosine, and tangent. They answer the question of what angle produces a given trigonometric value. The most common arcs functions are arcsine (or inverse sine, denoted as arcsin or sin⁻¹), arccosine (or inverse cosine, denoted as arccos or cos⁻¹), and arctangent (or inverse tangent, denoted as arctan or tan⁻¹).

The arcsine function, arcsin(x), returns an angle θ such that sin(θ) = x. Its domain is [-1, 1] and its principal range is typically [-π/2, π/2] radians or [-90°, 90°]. The arccosine function, arccos(x), returns an angle θ such that cos(θ) = x. Its domain is also [-1, 1], but its principal range is usually [0, π] radians or [0°, 180°]. The arctangent function, arctan(x), returns an angle θ such that tan(θ) = x. Its domain is all real numbers (-∞, ∞), and its principal range is typically (-π/2, π/2) radians or (-90°, 90°).

These functions are essential in trigonometry and calculus, particularly when solving trigonometric equations or when dealing with problems involving angles derived from ratios. They are also used in physics and engineering to calculate angles in various scenarios. Understanding their domains and principal ranges is crucial to avoid ambiguity and ensure correct application.