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10th Edition

Ron Larson + 1 other

ISBN: 9781285057095

Textbook Problem

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CardioidsConsider the cardioids

as shown in the figure. Let
*natural equation* for the curve.)

To determine

**To prove:** The *s* and

Explanation

**Given:** Thecardioids equation is,

**Proof:** The one arch of the cycloid is,

As,

And

Here,

Considering the function,

Differentiating the above given function,

Considering the function

Differentiating the above function,

The magnitude of position vector,

Simplifying the above equation,

From the given condition, the arc length between the point

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