The spherical coordinates of (-3, 4,-12) are (ρ,ϴ,Φ). Find tanϴ+tanΦ ?

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Answer 1 · 2018-06-21T08:28:41

Please see the explanation below.

The spherical coordinates #(rho, theta, phi)# are related to the rectangular coordinates #(x,y,z)# by

#{(x=rhocostheta),(y=rhosintheta),(z=rhocosphi):}#

Here #{(x=-3),(y=4),(z=-12):}#

#rho=sqrt((-3)^2+(4)^2+(-12)^2)=sqrt(169)=13#

#tantheta=y/x=4/(-3)=-4/3#

#cosphi=z/rho=-12/13#

#tan^2phi+1=1/cos^2phi=169/144#

#tan^2phi=169/144-1=25/144#

#tanphi=+-5/12#

Therefore,

#tantheta+tanphi=-4/3+5/12=-11/12#

or

#tantheta+tanphi=-4/3-5/12=-21/12#