Question

Describe and sketch the surface of equation \(z = \sin y\)

Short answer

The surface of equation \(z = \sin y\) is described and sketched.

Step-by-step solution

Represent the Surface of Equations

The equation\(z = \sin y\)represents\(\{ (x,y,z)\mid z = \sin y\} \)and does not involve\(x\)-coordinates. Hence, set the\(x\)plane equation as\(z = \sin y\), where\(k\)is a constant.

Therefore, the resultant curve of equation \(z = \sin y\) forms a cylindrical surface with a duplicate of the same cylinder in plane \(x = k\).

The rulings in representation of \(z = \sin y\) are parallel to the \(x\)-axis.

The sketch of equation \(z = \sin y\) is shown below.

Thus, the surface of equation \(z = \sin y\) is described and sketched.