Introduction to Cylindrical Coordinates | Summary and Q&A

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May 26, 2019
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The Math Sorcerer
Introduction to Cylindrical Coordinates

TL;DR

Cylindrical coordinates are an extension of polar coordinates and are used to represent points in three-dimensional space.

Key Insights

• 😥 Cylindrical coordinates are used to represent points in three-dimensional space.
• 🐻‍❄️ The conversion from cylindrical to rectangular coordinates involves using formulas similar to the conversion from polar to rectangular coordinates.
• 😀 Similarly, the conversion from rectangular to cylindrical coordinates involves using formulas that relate the rectangular coordinates to the values of r, theta, and z.

Transcript

hi everyone in this video we're going to talk about cylindrical coordinates so cylindrical coordinates coordinates so cylindrical coordinates are an extension of polar coordinates so let's go through this very very carefully so first a point P which we can call X Y Z and rectangular is represented represented by another ordered triple except this t... Read More

Q: What are cylindrical coordinates?

Cylindrical coordinates are an extension of polar coordinates, representing a point in three-dimensional space using the ordered triple (r, theta, z), where r and theta come from polar coordinates and z is the directed distance from the point to the xy-plane.

Q: How do you convert from cylindrical to rectangular coordinates?

To convert from cylindrical to rectangular coordinates, you can use the formulas X = rcos(theta), Y = rsin(theta), and Z = z. These formulas allow you to convert the values of r, theta, and z into their corresponding rectangular coordinates.

Q: What are the formulas for converting from rectangular to cylindrical coordinates?

The formulas for converting from rectangular to cylindrical coordinates are r = sqrt(X^2 + Y^2), theta = arctan(Y/X), and z = Z. These formulas allow you to determine the values of r, theta, and z based on the given rectangular coordinates X, Y, and Z.

Q: Is the representation of cylindrical coordinates unique?

No, the representation of cylindrical coordinates is not unique. Angle theta can have multiple values, differing by multiples of 2*pi. Therefore, there can be multiple representations of the same point in cylindrical coordinates.

Summary & Key Takeaways

• Cylindrical coordinates are an extension of polar coordinates, representing a point as (r, theta, z), where r and theta are from polar coordinates and z is the directed distance from the point to the xy-plane.

• Converting from cylindrical to rectangular coordinates can be done using the formulas X = rcos(theta), Y = rsin(theta), and Z = z.

• Converting from rectangular to cylindrical coordinates can be done using the formulas r = sqrt(X^2 + Y^2), theta = arctan(Y/X), and z = Z.