Sketching an Unusual Cylinder Draw a graph of the surface [latex]z=\sin x \text { in } R ^3[/latex].

In this case, there are no y’s in the equation. Consequently, traces of the surface in any plane parallel to the [latex]x z \text {-plane }[/latex] are the same; they all look like the two-dimensional graph of [latex]z=\sin x \text {. We draw one of these in the } x z \text {-plane }[/latex] and then make copies in planes parallel to the [latex]x z \text {-plane }[/latex] plane, finally connecting the traces with lines parallel to the y-axis. (See Figure 10.54a.) In Figure 10.54b, we show a computer-generated wireframe plot of the same surface. In this case, the cylinder looks like a plane with ripples in it.

Question 10.6.2: Sketching an Unusual Cylinder Draw a graph of the surface z ...

Calculus: Early Transcendental Functions

Sketching an Unusual Cylinder

Draw a graph of the surface $z=\sin x \text { in } R ^3$ .

The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

In this case, there are no y’s in the equation. Consequently, traces of the
surface in any plane parallel to the $x z \text {-plane }$ are the same; they all look like the two-dimensional graph of $z=\sin x \text {. We draw one of these in the } x z \text {-plane }$ and then make copies in planes parallel to the $x z \text {-plane }$ plane, finally connecting the traces with lines parallel to the y-axis. (See Figure 10.54a.) In Figure 10.54b, we show a computer-generated wireframe plot of the same surface. In this case, the cylinder looks like a plane with ripples in it.