Question

Convert the spherical coordinates (√3, - ∏/2 , ∏/3) to rectangular coordinates.

a) (0, √3, -√3/2)
b) (√3, 0, -√3/2)
c) (√3/2, -√3/2, 0)
d) (0,- √3, √3/2)

Answer 1

To convert spherical coordinates to rectangular coordinates, use the formulas x = r * sin(phi) * cos(theta), y = r * sin(phi) * sin(theta), and z = r * cos(phi). Plugging in the given spherical coordinates, we get the answer as (0, sqrt(3), -sqrt(3)/2).

Step-by-step explanation:

To convert spherical coordinates to rectangular coordinates, we can use the following formulas:

x = r * sin(phi) * cos(theta)
y = r * sin(phi) * sin(theta)
z = r * cos(phi)

In this case, the spherical coordinates are (sqrt(3), -pi/2, pi/3). Let's plug them into the formulas:

x = sqrt(3) * sin(-pi/2) * cos(pi/3) = 0
y = sqrt(3) * sin(-pi/2) * sin(pi/3) = sqrt(3)
z = sqrt(3) * cos(-pi/2) = -sqrt(3)/2

Therefore, the rectangular coordinates are (0, sqrt(3), -sqrt(3)/2). Answer choice (b) matches the result.