Convert $( 1,1 , \sqrt { 2 } )$ from rectangular coordinates to spherical coordinates.
A) $\left( \sqrt { 2 } , \frac { \pi } { 4 } , \frac { \pi } { 4 } \right)$
B) $\left( 2 , \frac { \pi } { 4 } , \frac { \pi } { 4 } \right)$
C) $\left( \sqrt { 2 } , \frac { \pi } { 2 } , \frac { \pi } { 4 } \right)$
D) $\left( 2 , \frac { \pi } { 2 } , \frac { \pi } { 4 } \right)$
E) $\left( \sqrt { 2 } , \frac { \pi } { 4 } , \frac { \pi } { 2 } \right)$
F) $\left( 2 , \frac { \pi } { 4 } , \frac { \pi } { 2 } \right)$
G) $\left( \sqrt { 2 } , \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$
H) $\left( 2 , \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$

Question

Convert $( 1,1 , \sqrt { 2 } )$ from rectangular coordinates to spherical coordinates.
A) $\left( \sqrt { 2 } , \frac { \pi } { 4 } , \frac { \pi } { 4 } \right)$ 
B) $\left( 2 , \frac { \pi } { 4 } , \frac { \pi } { 4 } \right)$ 
C) $\left( \sqrt { 2 } , \frac { \pi } { 2 } , \frac { \pi } { 4 } \right)$ 
D) $\left( 2 , \frac { \pi } { 2 } , \frac { \pi } { 4 } \right)$ 
E) $\left( \sqrt { 2 } , \frac { \pi } { 4 } , \frac { \pi } { 2 } \right)$ 
F) $\left( 2 , \frac { \pi } { 4 } , \frac { \pi } { 2 } \right)$ 
G) $\left( \sqrt { 2 } , \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$ 
H) $\left( 2 , \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$

Quizplus · Accepted Answer

The spherical coordinates $(r, \theta, \phi)$ are calculated as follows: $r = \sqrt{x^2 + y^2 + z^2} = \sqrt{1^2 + 1^2 + (\sqrt{2})^2} = 2$, $\theta = \tan^{-1}(y/x) = \tan^{-1}(1/1) = \pi/4$, and $\phi = \cos^{-1}(z/r) = \cos^{-1}(\sqrt{2}/2) = \pi/4$.

Convert (1,1,2)( 1,1 , \sqrt { 2 } )(1,1,2​) From Rectangular Coordinates to Spherical Coordinates

Convert $( 1,1 , \sqrt { 2 } )$ From Rectangular Coordinates to Spherical Coordinates