 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-2/2/b/solution

For spherical coordinates, the distance from the origin is

26

and the polar angle satisfies

cos θ = z / r = - 1/ 26

. The azimuth is the same as in part (a). Thus

(r, θ, ϕ) = (26, arccos (- \frac{1}{26}), π + arctan \frac{4}{3}) .

(π /2, π)

because the point lies below the

x y

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