What are the rectangular coordinates of the point whose cylindrical coordinates are (r = 0, theta...

Question:

What are the rectangular coordinates of the point whose cylindrical coordinates are {eq}(r = 0, \; \theta = 4.4, \; z = -1) {/eq}?

Cylindrical Coordinate System:

Cylindrical coordinate System is a generalization of two-dimensional polar coordinate system to three dimensions by superposing a height z-axis.

If P is a point in the space, let r be the distance from the z-axis to P, {eq}\theta {/eq} be the angle (usually measured in radians) between the positive x-axis and the line from the origin to the projection of P on the xy-plane, z be the z-coordinate of P.

Then the point P is represented by the ordered triple {eq}(r, \theta, z) {/eq} and {eq}r, \theta,z {/eq} are called cylindrical coordinates.

The connection between cylindrical and Cartesian coordinates is given by the following equations.

{eq}x = r\cos \theta, \ y = r\sin \theta, \ z=z {/eq}

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Cylindrical & Spherical Coordinates: Definition, Equations & Examples

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Chapter 13 / Lesson 10
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Learn how to convert between Cartesian, cylindrical and spherical coordinates. Discover the utility of representing points in cylindrical and spherical coordinates.


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