Chapter 13: Q 7 (page 1065)

. To convert from rectangular to cylindrical coordinates:
$r =____, θ =_, z =_____$

Short Answer

Expert verified

$r = \sqrt{x^{2} + y^{2}} θ = \tan^{- 1} (\frac{y}{x}) z = z$

Step by step solution

Step 1:Given information

Given (x,y,z) are rectangular cooedinates and $(r, θ, z)$ are cylindrical coordinates

Step 2:Simplification

$(x, y, z)$ are rectangular coordinates and $(r, θ, z)$ are cylindrical coordinates

The relation is as below:

From the figure

$\Rightarrow \cos θ = \frac{x}{r}, \sin θ = \frac{y}{r}$

Now,

$\Rightarrow \cos^{2} θ + \sin^{2} θ = \frac{x^{2}}{r^{2}} + \frac{y^{2}}{r^{2}}$

$\Rightarrow r^{2} (\sin^{2} θ + \cos^{2} θ) = x^{2} + y^{2}$

$\Rightarrow r^{2} = x^{2} + y^{2}$

$\Rightarrow r = \sqrt{x^{2} + y^{2}}$

Similarly

$\frac{\sin θ}{\cos θ} = \frac{y}{x}$

$\Rightarrow \tan θ = \frac{y}{x}$

$\Rightarrow θ = \tan^{- 1} \frac{y}{x}$

And from the figure we can observe $z = z$

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. To convert from rectangular to cylindrical coordinates:
$r =____, θ =_, z =_____$

Short Answer

Step by step solution

Step 1:Given information

Step 2:Simplification

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. To convert from rectangular to cylindrical coordinates:r=______,θ=_____,z=_______

Short Answer

Step by step solution

Step 1:Given information

Step 2:Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Probability and Statistics

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Decision Maths

Study anywhere. Anytime. Across all devices.

. To convert from rectangular to cylindrical coordinates:
$r =____, θ =_, z =_____$