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Chapter 13: Q 25. (page 1066)

Give the rectangular and spherical coordinates for the point with cylindrical coordinates:

48,蟺3,4

Short Answer

Expert verified

Rectangular coordinates are23,6,4and spherical coordinates are8,蟺3,蟺3

Step by step solution

01

Given Information

The given expression isr,胃,蠒=48,蟺3,4

02

Finding the rectangular coordinates

As r=48,胃=蟺3,蠒=4

To find out rectangular coordinates, we will use

x=rcos胃,y=rsin胃,z=z

Using the values

x=48cos蟺3,y=48sin蟺3,z=4

x=23,y=6,z=4

x,y,z=23,6,4

03

Finding the spherical coordinates

To convert rectangular to spherical coordinates

蚁=r2+z2,胃=胃,蠒=tan-1rz

Putting the values

蚁=482+42,胃=蟺3,蠒=tan-1484

蚁=48+16,胃=蟺3,蠒=tan-13

鈬�蚁=64,胃=蟺3,蠒=蟺3

鈬�蚁=8,胃=蟺3,蠒=蟺3

鈬�蚁,胃,蠒=8,蟺3,蟺3

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