calculate Mathematics Topic: Trigonometry & Functions Subtopic: Unit Circle & Sine Wave Level: grade 9 10 Difficulty: intermediate ⏱ 15 mins

Trigonometric Unit Circle & Sine Wave Dynamic Visualizer

Dynamic geometric visualization of trigonometric ratios and sine waves.

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Unit Circle Foundation

In a circle with radius $r = 1$ centered at $(0,0)$, any point on the circumference has coordinates:

$$(x, y) = (costheta, sintheta)$$

As $theta$ sweeps from $0^circ$ to $360^circ$, the $y$-projection traces the fundamental periodic function $f(theta) = sintheta$.

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