What are the cylindrical coordinates of the point whose rectangular coordinates are #(x=-4, y=4, z=3)#?

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Answer 1 · 2016-12-05T15:13:07

The cylindrical coordinates are #(4sqrt2, (3pi)/4,3)#

To convert from rectangular coordinates #(x,y,z)# to cylindrical coordinates #(r,theta,z)#, we use the following

#x=rcostheta#

#y=rsin theta#

#r=sqrt (x^2+y^2)#

Here, #(x,y,z)=(-4,4,3)#

#r=sqrt(4^2+4^2)=sqrt(32)=4sqrt2#

#costheta=x/r=-4/(4sqrt2)=-1/sqrt2#

#theta=arccos(-1/sqrt2)=(3pi)/4#

So, the cylindrical coordinates are #(4sqrt2, (3pi)/4,3)#