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Convert the point from rectangular coordinates to cylindrical coordinates. (6, 2 3 , −9)

User Josh Noe
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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

User Flowstoneknight
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