$\mathrm{\ρ}\=\sqrt{2^2\+5^2\+3^2}\=\sqrt{38}$ ≐ 6.16

$\mathrm{\φ}\=\arccos \left(3\/\sqrt{38}\right)$ ≐ 1.06

$\mathrm{\θ}\=\arctan \left(5\/2\right)$ ≐ 1.19

$\genfrac{}{}{0ex}{}{\left[\sqrt{x^2\+y^2\+z^2}\,{\cos }^{-1}\left(\frac{z}{\sqrt{x^2\+y^2\+z^2}}\right)\,{\tan }^{-1}\left(\frac{y}{x}\right)\right]}{\phantom{x\=a}}|\genfrac{}{}{0ex}{}{\phantom{\mathrm{f(x)}}}{x\=2\,y\=5\,z\=3}$

$\left[\sqrt{38}\,\arccos \left(\frac{3}{38}\sqrt{38}\right)\,\arctan \left(\frac{5}{2}\right)\right]$

$\stackrel{\text{at 5 digits}}{\to }$

$\left[6.1644\,1.0625\,1.1903\right]$

$q≔\mathrm{eval}\left(\left[\sqrt{x^2\+y^2\+z^2}\,\arccos \left(z\/\sqrt{x^2\+y^2\+z^2}\right)\,\arctan \left(y\/x\right)\right]\,\left[x\=2\,y\=5\,z\=3\right]\right)$

$\left[\sqrt{38}\,\arccos \left(\frac{3}{38}\sqrt{38}\right)\,\arctan \left(\frac{5}{2}\right)\right]$

$\mathrm{evalf}\left(q\right)$

$\left[6.164414003\,1.062529081\,1.190289950\right]$

Initialize

$$\begin{gathered} \mathrm{with}\left(\mathrm{Student}:-\mathrm{VectorCalculus}\right)\: \\ \mathrm{BasisFormat}\left(\mathrm{false}\right)\: \end{gathered}$$

Change to spherical coordinates

$\mathbf{P}≔\mathrm{MapToBasis}\left(⟨2\,5\,3⟩\,\mathrm{spherical}\right)$

$\mathrm{evalf}\left(\mathbf{P}\right)$ = $$