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Chapter 13: Q 27. (page 1066)

Give the rectangular and cylindrical coordinates for the point with spherical coordinates8,蟺2,蟺

Short Answer

Expert verified

Rectangular coordinates arex,y,z=0,0,-8

Cylindrical coordinates arelocalid="1651612310902" r,胃,z=0,蟺2,-8

Step by step solution

01

Given Information

The given expression is 蚁,胃,蠒=8,蟺2,蟺

02

To find rectangular coordinates

As 蚁=8,胃=蟺2,蠒=蟺

We know that for converting spherical to rectangular coordinates,

x=蚁sin蠒cos胃,y=蚁sin蠒sin胃,z=蚁cos蠒

Using values given, we get

localid="1652288939533" x=8蝉颈苍蟺肠辞蝉蟺2,y=8蝉颈苍蟺蝉颈苍蟺2,z=8肠辞蝉蟺

x=800,y=801,z=8-1

x=0,y=0,z=-8

Hence, required coordinate arex,y,z=0,0,-8

03

To find cylindrical coordinates

To find cylindrical coordinates, we get

r=蚁sin蠒,胃=胃,z=蚁cos蠒

Substituting spherical coordinates, we get

role="math" localid="1652289128136" r=8蝉颈苍蟺,胃=蟺2,z=8肠辞蝉蟺

r=80,胃=蟺2,z=8-1

鈬�r=0,胃=蟺2,z=-8

Hence, cylindrical coordinates arer,胃,z=0,蟺2,-8

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