To convert rectangular coordinates (x, y, z) to cylindrical coordinates (r, θ, z), we use the following formulas:
- r = √(x² + y²)
- θ = arctan(y/x)
- z = z (remains the same)
Given the rectangular coordinates x=4, y=4, z=3, we can calculate:
1. Calculate r:
r = √(4² + 4²) = √(16 + 16) = √32 = 4√2
2. Calculate θ:
θ = arctan(4/4) = arctan(1) = π/4 (or 45 degrees)
3. The z-coordinate remains the same:
z = 3
Therefore, the cylindrical coordinates of the point are:
(r, θ, z) = (4√2, π/4, 3)