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

Question

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

Quizplus · Accepted Answer

Cylindrical coordinates are given by $(r, \theta, z)$, where $r = \sqrt{x^2 + y^2}$, $\theta = \tan^{-1}\left(\frac{y}{x}\right)$, and $z = z$. For the point $(1,1,1)$, $r = \sqrt{1^2 + 1^2} = \sqrt{2}$, $\theta = \tan^{-1}\left(\frac{1}{1}\right) = \frac{\pi}{4}$, and $z = 1$.

Convert (1,1,1)( 1,1,1 )(1,1,1) From Rectangular Coordinates to Cylindrical Coordinates (2,π2,1)\left( \sqrt { 2 } , \frac { \pi } { 2 } , 1 \right)(2​,2π​,1)

Convert $( 1,1,1 )$ From Rectangular Coordinates to Cylindrical Coordinates $\left( \sqrt { 2 } , \frac { \pi } { 2 } , 1 \right)$