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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2011/paper-2/12/a/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2011 / Paper 2 / 12 / a / Solution by

Codex  0 2026-10-18

Using the physics convention for spherical coordinates, the polar angle

θ

is measured from positive

z

and the azimuth

ϕ

from positive

x

toward positive

y

. The Cartesian coordinates are

x = r sin θ cos ϕ, y = r sin θ sin ϕ, z = r cos θ .

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