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Chapter 13: Q 8 (page 1066)

To convert from cylindrical to rectangular coordinates:

x=____,y=____,z=____

Short Answer

Expert verified

x=ρcosθy=ρsinθz=z

Step by step solution

01

Step 1:Given information

Givenx,y,zare rectangular coordinates andρ,θ,zare cylindrical coordinates

02

Step 2:Simplification

ρ,θ,zare cylindrical coordinates and x,y,zare rectangular coordinates

The relation is as below:

From the figure

cosθ=xρ

role="math" localid="1653036479004" ⇒x=ρcosθ

Similarly

sinθ=yρ

⇒y=ρsinθ

And from the figure we can observez=z

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