If a circle C with radius 1 rolls along the outside of the circle x2 + y2 = 16, a fixed point P on C traces out a curve called an epicycloid, with parametric equations x = 5 cos t − cos 5t, y = 5 sin t − sin 5t. Graph the epicycloid and use (5) to find the area it encloses.
To find: The graph of epicycloid and the area it encloses.
Parametric equations of epicycloid are , and a circle .
Write the area of D using Green’s Theorem .
Draw the epicycloid as shown in Figure 1.
Consider the domain of epicycloid as .
Write the parametric equation of epicycloids.
Differentiate equation (2) with respect to t.
Substitute for x and for in equation (1),
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