 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-2/7/a/solution

Use the convention that

θ

is the polar angle from positive

z

, and

ϕ

the azimuth from positive

x

. The radius is

r = \frac{3}{16} + \frac{9}{16} + \frac{9}{4} = 3 .

Then

cos θ = z / r = 3 /2

, while

tan ϕ = y / x = 3

and both planar coordinates are positive. Thus the spherical coordinates are

(r, θ, ϕ) = (3, \frac{π}{6}, \frac{π}{3}) .

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