03 Jul, 2021 09:11 PM

Change from rectangular to cylindrical coordinates. (Let r ≥ 0 and 0 ≤ θ ≤ 2π.) (a) (−4, 4, 4) b) (−7, 7sqrt3,8)?

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Answer
Answer
AM
03 Jul, 2021 09:12 PM

x = r cosθ

y = r sinθ

x² + y² = r²

z = z

a.

(−4,4,4)

r² = 16 + 16 = 32

r = 4√2

cosθ = x/r = −1/√2

sinθ = y/r = 1/√2

θ = 3π/4

(r, θ, z) = (4√2, 3π/4, 4)

b.

(−7, 7√3, 8)

r² = 49 + 147 = 196

r = 14

cosθ = x/r = −1/2

sinθ = y/r = √3/2

θ = 2π/3

(r, θ, z) = (14, 2π/3, 8)