Convert the following equation to Cartesian: {eq}\rho - \sin \psi = 4 - \cos^{2} \psi {/eq}

Question:

Convert the following equation to Cartesian: {eq}\rho - \sin \psi = 4 - \cos^{2} \psi {/eq}

Cartesian Coordinates:

An equation in the form of spherical coordinates can be converted into the Cartesian equation. The relation between spherical and Cartesian coordinates is:

{eq}\begin{aligned} \rho &= \sqrt{x^2 + y^2 + z^2} \\ \cos\psi &= \frac{z}{\sqrt{x^2 + y^2 + z^2}} \end{aligned} {/eq}

Answer and Explanation: 1

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Given

{eq}\rho - \sin\psi = 4 - \cos^2\psi {/eq}

Convert the equation into Cartesian form.

{eq}\begin{aligned} \rho - \sqrt{1 - \cos^2\psi} &= 4...

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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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