Converting Rectangular Equations to Cylindrical Equations

This video tutorial demonstrates how to convert rectangular equations into cylindrical equations through four examples. It begins with an introduction to cylindrical coordinates, explaining the conversion process using substitutions for x and y. The tutorial covers various equations, including z equals x squared plus y squared minus two, y squared equals 10 minus z squared, x equals y squared, and x squared plus y squared equals six y. Each example illustrates the steps to achieve cylindrical form, emphasizing the importance of using trigonometric identities and simplification techniques.

What is the form of a point in cylindrical coordinates?

• (x, y, z)

• (r, θ, z)

• (r, θ, φ)

• (ρ, φ, θ)

In the equation z = x^2 + y^2 - 2, what substitution is used for x^2 + y^2?

• r^2

• r sin θ

• r cos θ

• r tan θ

When converting y^2 = 10 - z^2, what is y replaced with in cylindrical coordinates?

• r tan θ

• r sin θ

• r sec θ

• r cos θ

What is the simplified form of the equation y^2 = 10 - z^2 in cylindrical coordinates?

• z^2 = 10 - r^2 sec^2 θ

• z^2 = 10 - r^2 tan^2 θ

• z^2 = 10 - r^2 cos^2 θ

• z^2 = 10 - r^2 sin^2 θ

In the equation x = y^2, what is x replaced with in cylindrical coordinates?

• r sin θ

• r tan θ

• r sec θ

• r cos θ

What is the cylindrical form of the equation x = y^2?

• r = sec θ / tan^2 θ

• r = tan θ / sec^2 θ

• r = sin θ / cos^2 θ

• r = cos θ / sin^2 θ

What is the common form of the equation r = cos θ / sin^2 θ?

• r = sin θ cos θ

• r = tan θ sec θ

• r = cot θ csc θ

• r = sec θ tan θ

In the equation x^2 + y^2 = 6y, what substitution is used for x^2 + y^2?

• r cos θ

• r tan θ

• r^2

• r sin θ

What is the cylindrical form of the equation x^2 + y^2 = 6y?

• r = 6 sin θ

• r = 6 tan θ

• r = 6 cos θ

• r = 6 sec θ

What is the most common form for the cylindrical equation x^2 + y^2 = 6y?

• r = 6 sin θ

• r = 6 tan θ

• r = 6 cos θ

• r = 6 sec θ