How do you convert the point (3,-3, 7) from rectangular coordinates to cylindrical coordinates?

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How do you convert the point (3,-3, 7) from rectangular coordinates to cylindrical coordinates?

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Answer 1 · 2016-12-27T09:19:48

Cylindrical coordinates are $(3 \sqrt{2}, - \frac{π}{4}, 7)$ $(3sqrt2,-pi/4,7)$

Explanation:

The relation between rectangular coordinates (in $3$ $3$ -dimension) $(x, y, z)$ $(x,y,z)$ and cylindrical coordinates $(r, ϕ, z)$ $(r,phi,z)$ is

$r = \sqrt{x^{2} + y^{2}}$ $r=sqrt(x^2+y^2)$ , $ϕ = {tan}^{- 1} (\frac{y}{x})$ $phi=tan^(-1)(y/x)$ and $z = z$ $z=z$
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As rectangular coordinates are $(3, - 3, 7)$ $(3,-3,7)$ , we have

$r = \sqrt{3^{2} + {(- 3)}^{2}} = \sqrt{9 + 9} = \sqrt{18} = 3 \sqrt{2}$ $r=sqrt(3^2+(-3)^2)=sqrt(9+9)=sqrt18=3sqrt2$

$ϕ = {tan}^{- 1} (- \frac{3}{3}) = {tan}^{- 1} (- 1) = - \frac{π}{4}$ $phi=tan^(-1)(-3/3)=tan^(-1)(-1)=-pi/4$

Hence, cylindrical coordinates are $(3 \sqrt{2}, - \frac{π}{4}, 7)$ $(3sqrt2,-pi/4,7)$

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How do you convert the point (3,-3, 7) from rectangular coordinates to cylindrical coordinates?

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