Identify a basic trigonometric function from its graph features
Problem
Identify the basic trigonometric function shown as a smooth wave through the origin with period \(2\pi~\), and justify the identification from those features.
Identify a parent trig graph by combining features instead of relying on one familiar point. First use boundedness, smoothness, asymptotes, and repeat length to narrow the function family. Then inspect the value and direction at a key input such as the origin; together, those clues distinguish graphs that otherwise share the same wave shape.
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