$\"\"$

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Let $\"\"$ be the measure of the circle rotation.

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Let $\"\"$ begin at the $\"\"$ .

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When $\"\"$ , $\"\"$ is at maximum point $\"\"$ .

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When $\"\"$ , $\"\"$ is at maximum point $\"\"$ .

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When $\"\"$ , $\"\"$ is at maximum point $\"\"$ .

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Draw the figure :

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$\"\"$

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Observe the figure :

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The circle rolls along the $\"\"$ -axis then $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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The parametric equations are $\"\"$ and $\"\"$ .

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$\"\"$

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The parametric equations are $\"\"$ and $\"\"$ .