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Chapter 10: Q 23. (page 777)

Give the cylindrical and spherical coordinates for the point with rectangular coordinates(1,0,0)

Short Answer

Expert verified

Cylindrical coordinates are 1,0,0and spherical coordinates are1,0,蟺2

Step by step solution

01

Given Information

The given coordinates in rectangular coordinates are1,0,0

02

Finding the cylindrical coordinates

It is given thatx=1,y=0,z=0

We know that r=x2+y2,胃=tan-1yx,z=z

Substituting the values, we get

r=12+02,胃=tan-101,z=0

鈬�r=1,胃=0掳,z=0

localid="1651608209346" 鈬�r,胃,z=(1,0,0)

03

Finding the spherical coordinates

We know that 蚁=x2+y2+z2,胃=tan-1yx,蠒=cos-1zx2+y2+z2

鈬�蚁=12+02+02,胃=tan-101,蠒=cos-1012+02+02

鈬�蚁=1,胃=0掳,蠒=cos-10掳

鈬�蚁=1,胃=0掳,蠒=蟺2

鈬�蚁,胃,蠒=1,0,蟺2

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