Convert between the coordinate systems. Use the conversion formulas and show work. Spherical: (8,frac{pi}{3}, frac{pi}{6}) Change to cylindrical.

texelaare 2021-01-22 Answered
Convert between the coordinate systems. Use the conversion formulas and show work. Spherical: (8,π3,π6) Change to cylindrical.
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Expert Answer

Elberte
Answered 2021-01-23 Author has 95 answers

Solution: The spherical coordinates are given by (s,ϕ,ψ)

So here s=8,ϕ=π3,ψ=π6

These co-ordinates can be converted into culindrical coordinates by. r=ssinψ
ϕ=ϕ
z=scosψ

So,

r=8sin(π6),ϕ=π3,z=8cos(π6)

Thus,

r=812,ϕ=π3,z=832

Thus,

r=4,

ϕ=π3,

z=43

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