Final answer:
To convert (1, √3, 7) from rectangular coordinates to cylindrical coordinates, use the formulas r = sqrt(x^2 + y^2), θ = arctan(y/x), and z = z.
Step-by-step explanation:
To convert from rectangular coordinates to cylindrical coordinates, we use the formulas:
r = sqrt(x^2 + y^2)
θ = arctan(y/x)
z = z
In this case, the given rectangular coordinates are (1, √3, 7). Let's plug in the values:
r = sqrt(1^2 + (√3)^2) = sqrt(1 + 3) = sqrt(4) = 2
θ = arctan(√3/1) = arctan(√3) ≈ 60°
z = 7
Therefore, the cylindrical coordinates are (2, 60°, 7).