Question

Use a computer to graph the parametric surface. Get a printout and indicate on it which grid curves have u constant and which have v constant\(x = \sin v,y = \cos u\,\,\sin 4v,z = \sin 2u\,\,\sin 4v,0 \le u \le 2\pi , - \pi /2 \le v \le \pi /2\)

Short answer

The graph of the parametric surface

Step-by-step solution

Given information and corresponding results

\(\begin{array}{l}x = \sin v\\y = \cos u\sin 4v\\z = \sin 2u\sin 4v\end{array}\)

Let, u be a constant. Then the corresponding grid curves contained in \(z = ky\)planes and passes through the x axis.

Similarly, v constant we can obtain the grid curves are parallel to the yz-plane.

Graph of the parametric surface by using computer

Let us graph the parametric curve with parameter domain

\(0 \le u \le 2\pi \)and \(\frac{{ - \pi }}{2} \le v \le \frac{\pi }{2}\)