Converting Cylindrical to Cartesian Coordinates

The video tutorial explains how to convert cylindrical coordinates to Cartesian coordinates. It begins by introducing the given cylindrical coordinates and the formulas needed for conversion. The tutorial then demonstrates how to use a reference triangle and the unit circle to find trigonometric values. These values are verified on the unit circle, and the final Cartesian coordinates are calculated. The tutorial concludes with a discussion on using exact values versus decimal approximations.

What are the given values for r, theta, and z in the cylindrical coordinates?

• r = 3, theta = 7π/6, z = -4

• r = 3, theta = π/3, z = 4

• r = 4, theta = 5π/6, z = -3

• r = 2, theta = π/2, z = -1

Which formula is used to find the x-coordinate in Cartesian coordinates?

• x = r tan(theta)

• x = r cot(theta)

• x = r sin(theta)

• x = r cos(theta)

What is the formula for the y-coordinate in Cartesian coordinates?

• y = r cos(theta)

• y = r sin(theta)

• y = r tan(theta)

• y = r cot(theta)

In which quadrant does the angle 7π/6 radians terminate?

• First quadrant

• Third quadrant

• Fourth quadrant

• Second quadrant

What is the reference angle for 7π/6 radians?

• π/6 radians

• π/4 radians

• π/2 radians

• π/3 radians

What is the value of cosine(7π/6) using the reference triangle?

• -√3/2

• 1/2

• √3/2

• -1/2

What is the value of sine(7π/6) using the reference triangle?

• √3/2

• -1/2

• -√3/2

• 1/2

What is the x-coordinate in Cartesian coordinates after conversion?

• 3/2

• -3/2

• 3√3/2

• -3√3/2

What is the y-coordinate in Cartesian coordinates after conversion?

• √3/2

• -3/2

• -√3/2

• 3/2

Why might one prefer to use exact values over decimal approximations?

• Decimal approximations are less accurate.

• Exact values are more precise.

• Decimal approximations are more precise.

• Exact values are easier to calculate.