 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/a/solution

r = x^{2} + y^{2} = 5

and

z = - 1

. The point is in the third quadrant, so a representative azimuth in

[0, 2 π)

π + arctan (4/3)

. Therefore

(r, θ, z) = (5, π + arctan \frac{4}{3}, - 1) .

The angle is defined modulo

2 π

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