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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=zcosฮธ+sinฮธ

And the spherical equation iscotฯ•=cosฮธ+cosฯ•

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=rcosฮธ,y=rsinฮธ

so,

z=x+y

โ‡’z=rcosฮธ+rsinฮธ

โ‡’r=zcosฮธ+sinฮธ

Therefore the cylindrical system is r=zcosฮธ+sinฮธ

Now,

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

x=ฯsinฯ•cosฮธ,y=ฯsinฯ•cosฯ•,z=cosฯ•

so,

z=x+y

โ‡’ฯcosฯ•=ฯsinฯ•cosฮธ+ฯsinฯ•cosฯ•

โ‡’ฯcosฯ•=ฯsinฯ•cosฮธ+cosฯ•

โ‡’ฯcosฯ•ฯsinฯ•=cosฮธ+cosฯ•

โ‡’cotฯ•=cosฮธ+cosฯ•

Therefore the equation in spherical system iscotฯ•=cosฮธ+cosฯ•

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