FizeauV

2021-03-11

Convert the point from spherical coordinates to rectangular coordinates.

$(9,\pi ,\frac{\pi}{2})$

$(x,y,z)=?$

Laith Petty

Skilled2021-03-12Added 103 answers

Step 1

There are three coordinate systems and one coordinate system can be converted to other using the various conversion formulas.

The three coordinate systems are:

1) Rectangular coordinate system

2) Spherical coordinate system

3) Cylindrical coordinate system

Step 2

According to the question the spherical coordinates given are$(9,\pi ,\frac{\pi}{2}).$

Using the formulae:

the corresponding rectangular coordinates can be calculated as:

$x=p\mathrm{sin}\varphi \mathrm{cos}\theta $

$y=p\mathrm{sin}\varphi \mathrm{sin}\theta $

$z=p\mathrm{cos}\varphi $

Step 3

$p=9$

$\varphi =\frac{\pi}{2}$

$\theta =\pi $

$x=9.\mathrm{sin}\frac{\pi}{2}\mathrm{cos}\pi $

$x=9.1.-1$

$x=-9$

$y=9.\mathrm{sin}\frac{\pi}{2}.\mathrm{sin}\pi $

$y=9.1.0$

$y=0$

Step 4

$z=9.0$

$z=0$

so the rectangular coordinates are$(-9,0,0)$

There are three coordinate systems and one coordinate system can be converted to other using the various conversion formulas.

The three coordinate systems are:

1) Rectangular coordinate system

2) Spherical coordinate system

3) Cylindrical coordinate system

Step 2

According to the question the spherical coordinates given are

Using the formulae:

the corresponding rectangular coordinates can be calculated as:

Step 3

Step 4

so the rectangular coordinates are

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