   Chapter 10.2, Problem 47E

Chapter
Section
Textbook Problem

Graph the curve x = sin t + sin 1.5t, y = cos t and find its length correct to four decimal places.

To determine

To find: The length of the curve and plot the graph for the parametric equation x=sint+sin1.5t and y=cost .

Explanation

Given:

The parametric equation for the variable x is as follows.

x=sint+sin1.5t (1)

The parametric equation for the variable y is as follows.

y=cost (2)

Differentiate the parametric equation for the variable x .

x=sint+sin1.5tdxdt=cost+1.5cos1.5t

Differentiate the parametric equation for the variable y .

y=costdydt=sint

Substitute 3 for t in equation (1).

x=3tt3=3(3)(3)3=927=18

Substitute t=3 in equation (2).

y=3t2=3(3)2=27

The values of x and y for each step value of t is tabulated in the below table.

 t −169π −149π −43π −109π −89π −23π −49π −29π 0 −29π x −0.223 0.118 0.866 1.208 0.524 −0.866 −1.185 −1.508 0 0.766 y 1 0.173 1

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