   Chapter 13.1, Problem 38E

Chapter
Section
Textbook Problem

# Graph the curve with parametric equations x = sin t, y = sin 2t, z = cos 4t. Explain its shape by graphing its projections onto the three coordinate planes.

To determine

To sketch: The graph of the curve with parametric equations x=sint, y=sin2t, and z=cos4t explain the shape of projection onto three coordinate planes of parametric equations x=sint, y=sin2t, and z=cos4t.

Explanation

The parametric equations are x=sint, y=sin2t, and z=cos4t.

Draw the table with the values of parametric equations for t values in the interval [π2,π2] as shown below in Table 1.

 t x=sint y=sin2t z=cos4t −π2 –1 –1.2E-16 1 −π4 –0.70711 –1 –1 0 0 0 1 π4 0.707107 1 –1 π2 1 1.23E-16 1

Table 1

From Table 1, sketch the three-dimensional graph of parametric equations x=sint, y=sin2t, and z=cos4t as shown below in Figure 1

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