91Ó°ÊÓ

For the following exercises, the equation of a surface in rectangular coordinates is given. Find the equation of the surface in cylindrical coordinates. $$y=2 x^{2}$$

For the following exercises, the equation of a surface in rectangular coordinates is given. Find the equation of the surface in cylindrical coordinates. $$x^{2}+y^{2}-16 x=0$$

For the following exercises, the equation of a surface in rectangular coordinates is given. Find the equation of the surface in cylindrical coordinates. $$x^{2}+y^{2}-3 \sqrt{x^{2}+y^{2}}+2=0$$

For the following exercises, the spherical coordinates \((\rho, \theta, \varphi)\) of a point are given. Find the rectangular coordinates \((x, y, z)\) of the point. $$(3,0, \pi)$$

For the following exercises, the spherical coordinates \((\rho, \theta, \varphi)\) of a point are given. Find the rectangular coordinates \((x, y, z)\) of the point. $$\left(1, \frac{\pi}{6}, \frac{\pi}{6}\right)$$

For the following exercises, the spherical coordinates \((\rho, \theta, \varphi)\) of a point are given. Find the rectangular coordinates \((x, y, z)\) of the point. $$\left(12,-\frac{\pi}{4}, \frac{\pi}{4}\right)$$

For the following exercises, the spherical coordinates \((\rho, \theta, \varphi)\) of a point are given. Find the rectangular coordinates \((x, y, z)\) of the point. $$\left(3, \frac{\pi}{4}, \frac{\pi}{6}\right)$$

For the following exercises, the rectangular coordinates \((x, y, z)\) of a point are given. Find the spherical coordinates \((\rho, \theta, \varphi)\) of the point. Express the measure of the angles in degrees rounded to the nearest integer. $$(4,0,0)$$

For the following exercises, the rectangular coordinates \((x, y, z)\) of a point are given. Find the spherical coordinates \((\rho, \theta, \varphi)\) of the point. Express the measure of the angles in degrees rounded to the nearest integer. $$(-1,2,1)$$

For the following exercises, the rectangular coordinates \((x, y, z)\) of a point are given. Find the spherical coordinates \((\rho, \theta, \varphi)\) of the point. Express the measure of the angles in degrees rounded to the nearest integer. $$(0,3,0)$$