Question

What are the cylindrical coordinates of the point whose rectangular coordinates are (x = 1, y = 5, z = -1)?

Answer 1

To convert rectangular coordinates (x, y, z) to cylindrical coordinates (r, θ, z), use the formulas: r = √(x² + y²), θ = arctan(y/x), and z = z. Applying these formulas to the given rectangular coordinates (1, 5, -1), we find that the cylindrical coordinates are approximately (r ≈ √26, θ ≈ 1.37 radians, z = -1).

Step-by-step explanation:

To convert rectangular coordinates to cylindrical coordinates, we can use the following formulas:

• r = √(x² + y²)
• θ = arctan(y/x)
• z = z

In this case, the rectangular coordinates are (x = 1, y = 5, z = -1).

Using the formulas above:

• r = √(1² + 5²) = √26
• θ = arctan(5/1) = arctan(5) ≈ 1.37 radians
• z = -1

Therefore, the cylindrical coordinates of the point are (r ≈ √26, θ ≈ 1.37 radians, z = -1).