Convert $( 1 , \pi , \pi )$ from spherical coordinates to rectangular coordinates.
A) $( 0,0 , - 1 )$
B) $( 0,0,1 )$
C) $( 0,1 , - 1 )$
D) $( 1,0 , - 1 )$
E) $( 1,1 , - 1 )$
F) $( 1,0,1 )$
G) $( 0,1,1 )$
H) $( 1,1,1 )$

Question

Convert $( 1 , \pi , \pi )$ from spherical coordinates to rectangular coordinates.
A) $( 0,0 , - 1 )$ 
B) $( 0,0,1 )$
C) $( 0,1 , - 1 )$ 
D) $( 1,0 , - 1 )$ 
E) $( 1,1 , - 1 )$ 
F) $( 1,0,1 )$ 
G) $( 0,1,1 )$ 
H) $( 1,1,1 )$

Quizplus · Accepted Answer

The spherical coordinates $(\rho, \theta, \phi)$ can be converted to rectangular coordinates $(x, y, z)$ using the formulas $x = \rho \sin(\phi) \cos(\theta)$, $y = \rho \sin(\phi) \sin(\theta)$, and $z = \rho \cos(\phi)$. For $(1, \pi, \pi)$, we have $\rho = 1$, $\theta = \pi$, and $\phi = \pi$. Substituting these values, we get $x = 1 \sin(\pi) \cos(\pi) = 0$, $y = 1 \sin(\pi) \sin(\pi) = 0$, and $z = 1 \cos(\pi) = -1$. Therefore, the rectangular coordinates are $(0, 0, -1)$.

Convert (1,π,π)( 1 , \pi , \pi )(1,π,π) From Spherical Coordinates to Rectangular Coordinates

Convert $( 1 , \pi , \pi )$ From Spherical Coordinates to Rectangular Coordinates