The rectangular coordinates of the given cylindrical coordinates $\left( 2 , \frac { \pi } { 6 } , - 5 \right)$ are

A) $( 2 , - 1 , - 5 )$
B) $( \sqrt { 3 } , 1 , - 5 )$
C) $( \sqrt { 2 } , 1 , - 5 )$
D) $( \sqrt { 5 } , 1 , - 5 )$
E) $( 2,1 , - 5 )$

Question

The rectangular coordinates of the given cylindrical coordinates $\left( 2 , \frac { \pi } { 6 } , - 5 \right)$ are

A) $( 2 , - 1 , - 5 )$
B) $( \sqrt { 3 } , 1 , - 5 )$
C) $( \sqrt { 2 } , 1 , - 5 )$
D) $( \sqrt { 5 } , 1 , - 5 )$
E) $( 2,1 , - 5 )$

Quizplus · Accepted Answer

To convert from cylindrical coordinates $(r, \theta, z)$ to rectangular coordinates $(x, y, z)$, use the formulas $x = r \cos(\theta)$ and $y = r \sin(\theta)$. For $(2, \frac{\pi}{6}, -5)$, $x = 2 \cos(\frac{\pi}{6}) = 2 \times \frac{\sqrt{3}}{2} = \sqrt{3}$ and $y = 2 \sin(\frac{\pi}{6}) = 2 \times \frac{1}{2} = 1$, with $z = -5$. Thus, the rectangular coordinates are $(\sqrt{3}, 1, -5)$.

The Rectangular Coordinates of the Given Cylindrical Coordinates (2,π6,−5)\left( 2 , \frac { \pi } { 6 } , - 5 \right)(2,6π​,−5)

The Rectangular Coordinates of the Given Cylindrical Coordinates $\left( 2 , \frac { \pi } { 6 } , - 5 \right)$