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Chapter 11: Problem 93

Give the equations for the coordinate conversion from rectangular to cylindrical coordinates and vice versa.

Short Answer

Expert verified
The conversion from rectangular to cylindrical coordinates is given by \( r = \sqrt{x^2 + y^2} \), \( \theta = \tan^{-1} \left( \frac{y}{x} \right) \), and \( z = z \). And the conversion from cylindrical to rectangular coordinates is given by \( x = r \cos(\theta) \), \( y = r \sin(\theta) \), and \( z = z \).

Step by step solution

01

Conversion from Rectangular to Cylindrical Coordinates

The transformation from rectangular to cylindrical coordinates are given by the following formulas:\n1. \( r = \sqrt{x^2 + y^2} \) \n2. \( \theta = \tan^{-1} \left( \frac{y}{x} \right) \) \n3. \( z = z \)
02

Conversion from Cylindrical to Rectangular Coordinates

The transformation from cylindrical to rectangular coordinates can be done by the following formulas:\n1. \( x = r \cos(\theta) \) \n2. \( y = r \sin(\theta) \) \n3. \( z = z \)

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