Spherical Coordinates and Angle Determination

The video tutorial explains how to convert a point from Cartesian coordinates to spherical coordinates. It covers the calculation of the spherical coordinates rho, theta, and phi. The process involves determining the distance rho from the origin, finding the angle theta in the correct quadrant, and calculating the angle phi using inverse trigonometric functions. The tutorial emphasizes the importance of using a calculator in radian mode and provides step-by-step instructions for each calculation.

What are the Cartesian coordinates of the given point?

• x = -1, y = 3, z = 4

• x = 4, y = -3, z = 1

• x = 3, y = -4, z = 1

• x = -3, y = 4, z = -1

What is the formula used to calculate ρ in spherical coordinates?

• ρ = x² + y² - z²

• ρ = x + y + z

• ρ² = x² + y² + z²

• ρ² = x + y + z

What is the value of ρ for the point (-3, 4, -1)?

• √26

• √30

• √20

• √10

Which quadrant does the angle θ terminate in for the point (-3, 4)?

• Third quadrant

• Second quadrant

• Fourth quadrant

• First quadrant

What is the tangent of θ for the point (-3, 4)?

• -3/4

• 3/4

• -4/3

• 4/3

What is the approximate value of θ in radians?

• 0.9 radians

• 3.1 radians

• 1.5 radians

• 2.2 radians

Why is it important to sketch the point in the XY plane when determining θ?

• To find the value of z

• To ensure the angle is in the correct quadrant

• To determine the distance from the origin

• To calculate the exact value of ρ

What is the formula for calculating φ in spherical coordinates?

• cos φ = z / ρ

• sin φ = z / ρ

• tan φ = z / ρ

• φ = z / ρ

What is the approximate value of φ in radians?

• 3.0 radians

• 1.8 radians

• 2.5 radians

• 0.5 radians

What is the spherical coordinate representation of the point (-3, 4, -1)?

• (√26, 2.2, 1.8)

• (√30, 2.5, 1.5)

• (√20, 1.8, 2.2)

• (√26, 1.5, 2.5)