The cylindrical coordinates of the given rectangular coordinates (-1, $\sqrt { 3 }$ , 4) are

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

Question

The cylindrical coordinates of the given rectangular coordinates (-1, $\sqrt { 3 }$ , 4) are

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

Quizplus · Accepted Answer

The cylindrical coordinates (r, θ, z) can be found from the rectangular coordinates (x, y, z) using the formulas r = sqrt(x^2 + y^2) and θ = atan2(y, x). Here, r = sqrt((-1)^2 + (√3)^2) = 2, and θ = atan2(√3, -1) = 2π/3 because the point is in the second quadrant. The z-coordinate remains the same, so the correct answer is (2, 2π/3, 4).

The Cylindrical Coordinates of the Given Rectangular Coordinates (-1 3\sqrt { 3 }3​

The Cylindrical Coordinates of the Given Rectangular Coordinates (-1 $\sqrt { 3 }$