Final answer:
To find the equation for the plane y = x in cylindrical coordinates, we express x and y in terms of r and θ and find that θ must be π/4 or 5π/4.
Step-by-step explanation:
The student is asking to find an equation for the plane given by y = 1x in cylindrical coordinates. In cylindrical coordinates, we express points with coordinates (r, θ, z) where r is the radius, θ is the angle, and z is the height. To convert the given equation into cylindrical coordinates, we use the relationships between Cartesian coordinates (x, y, z) and cylindrical coordinates, where x = r × cos(θ) and y = r × sin(θ).
Given y = 1x, we can substitute the cylindrical relationships to get r × sin(θ) = r × cos(θ). This simplifies to sin(θ) = cos(θ), which occurs when θ = π/4 or 5π/4 (45° or 225°) in the standard position on the unit circle. So the equation in cylindrical coordinates does not change the fact that we are dealing with a plane, but it does specify that the plane consists of all points where the angle θ satisfies the above condition, independent of the values of r and z.