What are the cylindrical coordinates of the point whose rectangular coordinates are x=4, y=4, z=3?

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)