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The Cycloid Problem (PreCal)

A circle is rolled along a flat surface without slipping. A fixed point on the circle traces a curve through the plane. 1. Hit play to see this circle roll along the x-axis. Take a moment to try to sketch the curve A traces as the circle rolls. 2. Click the box next to "See the path of point A" to check your conjecture. 3. Click the box next to "Guess function". Use your knowledge of trigonometry and transformations to find a function whose graph is the path traced out by point A.