   Chapter 10.2, Problem 78E

Chapter
Section
Textbook Problem

# Translation of a Plane Curve Consider the parametric equations x = 8 cos t and y = 8 sin t .(a) Describe the curve represented by the parametric equations.(b) How does the curve represented by the parametric equations x = 8 cos t + 3   and   y = 8 sin t + 6 compare to the curve described in part (a)?(c) How does the original curve change when cosine and sine are interchanged?

(a)

To determine
The curve represented by the parametric equations x=8cost and y=8sint.

Explanation

Consider the provided parametric equations,

x=8cost and y=8sint

First take the equation x=8cost,

x=8costx2=(8cost)2

So,

x2=64cos2t …...…... (1)

Now, consider the second equation,

y=8sinty2=(8sint)2

So,

y2=64sin2t …...…... (2)

Now, add the equation (1) and (2)

(b)

To determine
The curve represented by the parametric equations x=8cost+3 and y=8sint+6.

(c)

To determine
The change in the original curve when cosine and sine are interchanged in the parametric equations x=8cost and y=8sint.

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