   Chapter 13.3, Problem 10E

Chapter
Section
Textbook Problem

# Graph the curve with parametric equations x = sin t, y = sin 2t, z = sin 3t. Find the total length of this curve correct to four decimal places.

To determine

To plot: The curve with parametric equations x=sint , y=sin2t , and z=sin3t and find the total length of the curve with four decimal places.

Explanation

Given data:

Consider the parametric equations.

x=sint (1)

y=sin2t (2)

z=sin3t (3)

Draw the required curve by using parametric equations in equations (1), (2) and (3) as shown in Figure 1.

The different view of curve in Figure 1 is drawn as shown in Figure 2.

Include a plot showing a tube of radius 0.07 around the curve as shown in Figure 3.

The complete curve is given by parameter interval [0,2π] .

The vector equation r(t) is,

r(t)=x,y,z

Substitute sint for x, sin2t for y, and sin3t for z,

r(t)=sint,sin2t,sin3t

Differentiate the equation with respect to t.

r(t)=cost,2cos2t,3cos3t

Take magnitude on both sides of the equation

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