The cylindrical coordinates of the given rectangular coordinates $\left( - 1,0 , \frac { 1 } { 2 } \right)$ are

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

Question

The cylindrical coordinates of the given rectangular coordinates $\left( - 1,0 , \frac { 1 } { 2 } \right)$ are

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

Quizplus · Accepted Answer

The cylindrical coordinates $(r, \theta, z)$ can be found from rectangular coordinates $(x, y, z)$ using the formulas $r = \sqrt{x^2 + y^2}$ and $\theta = \tan^{-1}\left(\frac{y}{x}\right)$. For the given point $(-1, 0, \frac{1}{2})$, $r = \sqrt{(-1)^2 + 0^2} = 1$, and $\theta = \tan^{-1}\left(\frac{0}{-1}\right) = \pi$ (since the point is on the negative x-axis), and $z = \frac{1}{2}$. Therefore, the cylindrical coordinates are $(1, \pi, \frac{1}{2})$.

The Cylindrical Coordinates of the Given Rectangular Coordinates (−1,0,12)\left( - 1,0 , \frac { 1 } { 2 } \right)(−1,0,21​)

The Cylindrical Coordinates of the Given Rectangular Coordinates $\left( - 1,0 , \frac { 1 } { 2 } \right)$