Converting Cartesian Coordinates to Spherical Coordinates

The video tutorial explains how to convert a point from Cartesian coordinates to spherical coordinates. It covers the calculation of rho, the distance from the origin, theta, the angle in the XY plane, and phi, the angle from the positive Z-axis. The tutorial includes step-by-step instructions and calculator usage to find these spherical coordinates accurately.

What are the Cartesian coordinates of the point that needs to be converted to spherical coordinates?

• (-2, 1, 5)

• (-2, -1, 5)

• (2, -1, 5)

• (2, 1, -5)

What is the formula used to calculate the radial distance (rho) in spherical coordinates?

• sqrt(x + y + z)

• x^2 + y^2 + z^2

• sqrt(x^2 + y^2 + z^2)

• x + y + z

What is the value of rho for the point (-2, -1, 5)?

• sqrt(35)

• sqrt(40)

• sqrt(25)

• sqrt(30)

In which quadrant does the angle Theta lie for the point (-2, -1) in the XY plane?

• First

• Second

• Third

• Fourth

What is the reference angle used to find Theta in the third quadrant?

• 1.0472 radians

• 0.7854 radians

• 0.5236 radians

• 0.4636 radians

What is the approximate value of Theta in radians after adjusting for the third quadrant?

• 3.6 radians

• 1.6 radians

• 2.6 radians

• 4.6 radians

What is the formula used to calculate the angle Phi in spherical coordinates?

• cos(Phi) = rho / z

• tan(Phi) = z / rho

• sin(Phi) = z / rho

• cos(Phi) = z / rho

What is the approximate value of Phi in radians for the given point?

• 0.7 radians

• 0.6 radians

• 0.5 radians

• 0.4 radians

What are the final spherical coordinates for the point (-2, -1, 5)?

• (sqrt(30), 4.6, 0.7)

• (sqrt(30), 1.6, 0.6)

• (sqrt(30), 2.6, 0.5)

• (sqrt(30), 3.6, 0.4)

What is the significance of the angle Phi in spherical coordinates?

• It is the angle in the XY plane.

• It is the angle from the positive z-axis.

• It is the angle from the positive y-axis.

• It is the angle from the negative z-axis.