The cylindrical coordinates of the given rectangular coordinates (0, 1, -3) are

A) $\left( 1 , \frac { \pi } { 6 } , - 3 \right)$
B) $\left( 1 , \frac { \pi } { 4 } , - 3 \right)$
C) $\left( 1 , \frac { \pi } { 3 } , - 3 \right)$
D) $\left( 1 , \frac { \pi } { 2 } , - 3 \right)$
E) $\left( - 1 , \frac { \pi } { 2 } , - 3 \right)$

Question

The cylindrical coordinates of the given rectangular coordinates (0, 1, -3) are

A) $\left( 1 , \frac { \pi } { 6 } , - 3 \right)$
B) $\left( 1 , \frac { \pi } { 4 } , - 3 \right)$
C) $\left( 1 , \frac { \pi } { 3 } , - 3 \right)$
D) $\left( 1 , \frac { \pi } { 2 } , - 3 \right)$
E) $\left( - 1 , \frac { \pi } { 2 } , - 3 \right)$

Quizplus · Accepted Answer

The cylindrical coordinates are given by $(r, \theta, z)$, where $r = \sqrt{x^2 + y^2}$, $\theta$ is the angle in the xy-plane from the positive x-axis, and $z$ is the same as in Cartesian coordinates. For the point (0, 1, -3), $r = \sqrt{0^2 + 1^2} = 1$, $\theta = \frac{\pi}{2}$ because the point lies on the positive y-axis, and $z = -3$. Therefore, the correct cylindrical coordinates are $\left( 1 , \frac { \pi } { 2 } , - 3 \right)$.

The Cylindrical Coordinates of the Given Rectangular Coordinates (0, 1 (1,π6,−3)\left( 1 , \frac { \pi } { 6 } , - 3 \right)(1,6π​,−3)

The Cylindrical Coordinates of the Given Rectangular Coordinates (0, 1 $\left( 1 , \frac { \pi } { 6 } , - 3 \right)$