The spherical coordinates of the given rectangular coordinates (1, -1, $\sqrt { 2 }$ ) are

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

Question

The spherical coordinates of the given rectangular coordinates (1, -1, $\sqrt { 2 }$ ) are

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

Quizplus · Accepted Answer

The spherical coordinates (ρ, θ, φ) can be found from the rectangular coordinates (x, y, z) using the formulas: ρ = sqrt(x^2 + y^2 + z^2), θ = atan2(y, x), and φ = acos(z / ρ). For (1, -1, sqrt(2)), ρ = sqrt(1^2 + (-1)^2 + (sqrt(2))^2) = sqrt(2 + 2) = sqrt(4) = 2, θ = atan2(-1, 1) = -π/4 (since in the fourth quadrant), and φ = acos(sqrt(2) / 2) = π/4.

The Spherical Coordinates of the Given Rectangular Coordinates (1, -1 2\sqrt { 2 }2​

The Spherical Coordinates of the Given Rectangular Coordinates (1, -1 $\sqrt { 2 }$