(a) The location of the point in Cartesian coordinates is (-2, 2√3, 3)
(b) The location of the point in spherical coordinates is (5, 2π/3, 0.93).
The Cartesian coordinates of the points is calculated as follows;
Points = (s, θ, z) = (4, 2π/3, 3)
x = scosθ
x = 4 x cos(2π/3)
x = 4 x cos(120)
x = 4 x (⁻¹/₂) = -2
y = s x sin(θ)
y = 4 x sin(2π/3)
y = 4 x sin(120)
y = 4 x (√3)/2 = 2√3
z = z = 3
Cartesian coordinates = (-2, 2√3, 3)
Points, = (p, θ, φ)
[tex]p = \sqrt{s^2 + z^2} \\\\p = \sqrt{4^2 + 3^2} = 5[/tex]
θ = 2π/3
[tex]\phi = cos^{-1} (\frac{z}{\sqrt{s^2 + z^2} } )\\\\\phi = cos^{-1} (\frac{3}{5} ) = 0.93 \ rad[/tex]
spherical coordinates = (5, 2π/3, 0.93)
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