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Convert (1, √ 3, 7) from rectangular coordinates to cylindrical coordinates.

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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).

User Koushik Goswami
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