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\(r(u,v) = \left( {u,\sin \left( {u + v} \right),\sin v} \right), - \pi \le u \le \pi , - \pi \le v \le \pi \)

Short answer

The graph of the parametric surface

Step-by-step solution

Apply the given equation to determine x, y, and z

By using the formula\(r(u,v) = (x,y,z)\),

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

Let, u be a constant. Then the corresponding grid curves are parallel to the xy-plane.

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

Graph of the parametric surface by using computer

Let us graph the parametric curve with parameter domain

\( - \pi \le u \le \pi \)and \( - \pi \le v \le \pi \)