Give the rectangular coordinates for the point with the cylindrical coordinates $\left( \sqrt { 2 } , \frac { \pi } { 4 } , 1 \right)$
A) $( 1,1,1 )$
B) $( 1,2,1 )$
C) $\left( 1 , \frac { 1 } { 2 } , 1 \right)$
D) $( 2,2,2 )$ d

Question

Quizplus · Accepted Answer

The conversion from cylindrical to rectangular coordinates is given by $x = r\cos(\theta)$, $y = r\sin(\theta)$, and $z = z$. For the given cylindrical coordinates $\left( \sqrt { 2 } , \frac { \pi } { 4 } , 1 \right)$, we have $x = \sqrt{2}\cos\left(\frac{\pi}{4}\right) = 1$, $y = \sqrt{2}\sin\left(\frac{\pi}{4}\right) = 1$, and $z = 1$, making the rectangular coordinates $(1,1,1)$.

Give the Rectangular Coordinates for the Point with the Cylindrical (2,π4,1)\left( \sqrt { 2 } , \frac { \pi } { 4 } , 1 \right)(2​,4π​,1)

Give the Rectangular Coordinates for the Point with the Cylindrical $\left( \sqrt { 2 } , \frac { \pi } { 4 } , 1 \right)$