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Describe the graphs of the equations in and provide alternative equations in the specified coordinate systems.

Changez=x+y to the cylindrical and spherical systems.

Short Answer

Expert verified

The cylindrical equation isr=zcosθ+sinθ

And the spherical equation iscotϕ=cosθ+cosϕ

Step by step solution

01

Step 1:Given information

The given expression isz=x+y

02

Step 2:Simplification

Consider the equation z=x+y

To change z=x+yinto cylindrical system,we can use

x=rcosθ,y=rsinθ

so,

z=x+y

z=rcosθ+rsinθ

r=zcosθ+sinθ

Therefore the cylindrical system is r=zcosθ+sinθ

Now,

to change z=x+yinto spherical system,we can use

x=ρsinϕcosθ,y=ρsinϕcosϕ,z=cosϕ

so,

z=x+y

ρcosϕ=ρsinϕcosθ+ρsinϕcosϕ

ρcosϕ=ρsinϕcosθ+cosϕ

ρcosϕρsinϕ=cosθ+cosϕ

cotϕ=cosθ+cosϕ

Therefore the equation in spherical system iscotϕ=cosθ+cosϕ

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