Final answer:
To convert a point from rectangular coordinates to cylindrical coordinates, use the formulas: r = sqrt(x^2 + y^2), θ = arctan(y/x), z = z. Substituting the given rectangular coordinates (6, 2, -9) into these formulas gives the cylindrical coordinates: r = 2sqrt(10), θ ≈ 18.43°, z = -9.
Step-by-step explanation:
To convert a point from rectangular coordinates to cylindrical coordinates, we can use the formulas:
r = sqrt(x^2 + y^2)
θ = arctan(y/x)
z = z
Using the given rectangular coordinates (6, 2, -9), we can substitute these values into the formulas to get the cylindrical coordinates:
r = sqrt(6^2 + 2^2) = sqrt(36 + 4) = sqrt(40) = 2sqrt(10)
θ = arctan(2/6) = arctan(1/3) ≈ 18.43°
z = -9