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

1 Answer
Shwetank Mauria
Dec 27, 2016

Cylindrical coordinates are #(3sqrt2,-pi/4,7)#

Explanation:

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

#r=sqrt(x^2+y^2)#, #phi=tan^(-1)(y/x)# and #z=z#
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As rectangular coordinates are #(3,-3,7)#, we have

#r=sqrt(3^2+(-3)^2)=sqrt(9+9)=sqrt18=3sqrt2#

#phi=tan^(-1)(-3/3)=tan^(-1)(-1)=-pi/4#

Hence, cylindrical coordinates are #(3sqrt2,-pi/4,7)#

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