Get the answer to "Convert the point from spherical coordinates to rectangular..."

FizeauV

Answered question

2021-03-11

Convert the point from spherical coordinates to rectangular coordinates.

(9, π, \frac{π}{2})

(x, y, z) = ?

Answer & Explanation

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, π, \frac{π}{2}) .

Using the formulae:
the corresponding rectangular coordinates can be calculated as:

x = p \sin ϕ \cos θ

y = p \sin ϕ \sin θ

z = p \cos ϕ

Step 3

p = 9

ϕ = \frac{π}{2}

θ = π

x = 9. \sin \frac{π}{2} \cos π

x = 9. 1. - 1

x = - 9

y = 9. \sin \frac{π}{2} . \sin π

y = 9. 1. 0

y = 0

Step 4

z = 9. 0

z = 0

so the rectangular coordinates are

(- 9, 0, 0)

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