Answer to Question #106870 in Analytic Geometry for khushi

Question

b) Find the cylindrical coordinates of the points where the Cartesian coordinates are (2)
i) (6,6,8)
ii) ( SQRT(2),1,1)

Answer 1

Transformation $(x,y,z)$ to $(\rho,\theta,z)$

$\rho=\sqrt{x^2+y^2}$

$\theta=tan^{-1}{\frac y x}$

$z=z$

i) $\rho=6\sqrt{2}$

$\theta=tan^{-1}1=\pi/4$

$z=8$

ii) $\rho=\sqrt{2+1}=\sqrt{3}$

$\theta=tan^{-1}{{\frac 1 {\sqrt2}}}$

$z=1$