Convert the following point from cylindrical coordinates to rectangular coordinates. $\left( 4 , \frac { \pi } { 3 } , 2 \right)$
A) $( 4,4 \sqrt { 3 } , 2 )$
B) $( 8,8 \sqrt { 3 } , 2 )$
C) $( 2 \sqrt { 3 } , 2,2 )$
D) $( 2,2 \sqrt { 3 } , 2 )$
E) $( 4 \sqrt { 3 } , 4,2 )$

Question

Quizplus · Accepted Answer

To convert from cylindrical to rectangular coordinates, we use the equations:

$x = r \cos 	heta$
$y = r \sin 	heta$
$z = z$

Plugging in the given values, we get:

$x = 4 \cos \frac{\pi}{3} = 2$
$y = 4 \sin \frac{\pi}{3} = 2\sqrt{3}$
$z = 2$

Therefore, the rectangular coordinates are $(2, 2\sqrt{3}, 2)$, which matches choice D.

Convert the Following Point from Cylindrical Coordinates to Rectangular Coordinates (4,π3,2)\left( 4 , \frac { \pi } { 3 } , 2 \right)(4,3π​,2)

Convert the Following Point from Cylindrical Coordinates to Rectangular Coordinates $\left( 4 , \frac { \pi } { 3 } , 2 \right)$