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

1 Answer
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)