Chapter 13: Q 4 (page 1065)

What are the graphs of the constant functions $r = r_{0}$
$θ = θ_{0}$ , and $z = z_{0}$ in the cylindrical coordinate system?

Short Answer

Expert verified

In the equation $θ = θ_{0}$ representing the plane parallel to $x z -$ plane.

and the equation $z = z_{0}$ representing the plane parallel to $x y -$ plane

Step by step solution

Given information

The goal is to understand the graphs of constant functions $r = r_{0}, θ = θ_{0}$ $z = z_{0}$ in cylindrical coordinates.

The graphs of $r = r_{0}$ represent plane equations parallel to the $y z$ -plane in the cylindrical coordinate system.

Determine whether the given equations are represented a coordinate system or not

The plane $x z$ - parallel to the -plane is represented by the equation $θ = θ_{0}$

The plane $x y -$ parallel to the -plane is represented by the equation $z = z_{0}$

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What are the graphs of the constant functions $r = r_{0}$
$θ = θ_{0}$ , and $z = z_{0}$ in the cylindrical coordinate system?

Short Answer

Step by step solution

Given information

Determine whether the given equations are represented a coordinate system or not

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What are the graphs of the constant functionsr=r0θ=θ0, andz=z0 in the cylindrical coordinate system?

Short Answer

Step by step solution

Given information

Determine whether the given equations are represented a coordinate system or not

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Most popular questions from this chapter

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Mechanics Maths

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What are the graphs of the constant functions $r = r_{0}$
$θ = θ_{0}$ , and $z = z_{0}$ in the cylindrical coordinate system?