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Chapter 13: Q 7 (page 1065)

. To convert from rectangular to cylindrical coordinates:

r=______,胃=_____,z=_______

Short Answer

Expert verified

r=x2+y2胃=tan-1yxz=z

Step by step solution

01

Step 1:Given information

Given (x,y,z) are rectangular cooedinates and r,胃,z are cylindrical coordinates

02

Step 2:Simplification

x,y,zare rectangular coordinates and r,胃,zare cylindrical coordinates

The relation is as below:

From the figure

鈬�cos胃=xr,sin胃=yr

Now,

鈬�cos2胃+sin2胃=x2r2+y2r2

鈬�r2sin2胃+cos2胃=x2+y2

鈬�r2=x2+y2

鈬�r=x2+y2

Similarly

sin胃cos胃=yx

鈬�tan胃=yx

鈬�胃=tan-1yx

And from the figure we can observez=z

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