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 $(ρ, θ, ϕ)$ $(rho, theta, phi)$ are related to the rectangular coordinates $(x, y, z)$ $(x,y,z)$ 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

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