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MATH / A point has rectangular coordinates (8,−3,−1) and spherical coordinates (ρ,θ,ϕ). Find the rectangular coordinates of the point with spherical coordinates (ρ,−θ,ϕ).

Problem

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problem

A point has rectangular coordinates (8,−3,−1)(8,-3,-1) and spherical coordinates (ρ,θ,ϕ).(\rho, \theta, \phi). Find the rectangular coordinates of the point with spherical coordinates (ρ,−θ,ϕ).(\rho, -\theta, \phi).
Plain-text mathematical notation (without MathML)
A point has rectangular coordinates (8,−3,−1) and spherical coordinates (ρ,θ,ϕ).  Find the rectangular coordinates of the point with spherical coordinates (ρ,−θ,ϕ).
Original LaTeX notation
A point has rectangular coordinates $(8,-3,-1)$ and spherical coordinates $(\rho, \theta, \phi).$  Find the rectangular coordinates of the point with spherical coordinates $(\rho, -\theta, \phi).$

level

Level 2

type

Precalculus

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Source and history

task_id
ff16cc00-f291-519b-b57e-2ba111de157c
task_key
precalculus--test--ff16cc00-f291-519b-b57e-2ba111de157c
task_revision_id
1
config / split
precalculus / test

Official source

initial import