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Describe the graphs of the equations and provide alternative equations in the specified coordinate system

. Changer=4sinθ to the rectangular and spherical systems.

Short Answer

Expert verified

The equation in rectangular system isx2+y2-4y=0

The equation in spherical system isρ=4cscϕsinθ

Step by step solution

01

Step 1:Given information

The given expression isr=4sinθ

02

SImplification

To convert r=4sinθinto rectangular coordinates systems as follows

substitute r=x2+y2and sinθ=yx2+y2in r=4sinθ

x2+y2=4yx2+y2

x2+y2-4y=0

Therefore the expression in rectangular system isx2+y2-4y=0

03

Step 3:Simplification

consider spherical coordinates as r=ρsinϕ,θ=θ,z=ρcosϕ

substituting r=ρsinϕin the equation r=4sinθ

ρsinϕ=4sinθ

ρ=4sinθsinϕ

ρ=4cscϕsinθ

Therefore the equation in spherical system isρ=4cscϕsinθ

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