Answer to Question #288860 in Analytic Geometry for Pankaj

Question

Find the cylindrical coordinates of the points where the Cartesian coordinates are :

(√5, 1,2)

Answer 1

Cylindrical coordinates $(r,\theta,z).$

$r=\sqrt{x^2+y^2}=\sqrt{\sqrt{5}^2+1^2}=\sqrt{6}.$

$\theta=arctan{\frac{y}{x}}=arctan{\frac{1}{\sqrt{5}}}=0.4205.$

$z=z=2.$

Cylindrical coordinates: $(\sqrt{6},0.4205,2).$