Final answer:
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).