# Describe in words the surface whose equation is given.\phi =\pi /3

Chesley 2021-09-19 Answered
Describe in words the surface whose equation is given.$\varphi =\frac{\pi }{3}$
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## Expert Answer

Viktor Wiley
Answered 2021-09-20 Author has 84 answers
$\varphi =\frac{\pi }{3}$ Spherical coordinates
$\mathrm{cos}\varphi =\mathrm{cos}\left(\frac{\pi }{3}\right)=\frac{1}{2}$ (1)$x=\rho \mathrm{sin}\varphi \mathrm{cos}0$
${\mathrm{cos}}^{2}\varphi =\frac{1}{4}$ (2)$y=\rho \mathrm{sin}\varphi \mathrm{sin}0$
${\rho }^{2}{\mathrm{cos}}^{2}\varphi =\frac{1}{4}{\rho }^{2}$ (3)$z=\rho \mathrm{cos}\varphi$
${z}^{2}=\frac{1}{4}\left({x}^{2}+{y}^{2}+{z}^{2}\right)$ (4)${x}^{2}+{y}^{2}+{z}^{2}={\rho }^{2}$
$4{z}^{2}={x}^{2}+{y}^{2}+{z}^{2}$
$3{z}^{2}={x}^{2}+{y}^{2}$
$3{z}^{2}={x}^{2}+{y}^{2}$ is a double cone, however, since the original equation $\varphi =\frac{\pi }{3}>0$, its
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