91Ó°ÊÓ

For the following exercises, the equation of a surface in rectangular coordinates is given. Find the equation of the surface in spherical coordinates. Identify the surface. \(x^{2}+y^{2}-3 z^{2}=0, \quad z \neq 0\)

For the following exercises, the equation of a surface in rectangular coordinates is given. Find the equation of the surface in spherical coordinates. Identify the surface. \(x^{2}+y^{2}+z^{2}-4 z=0\)

For the following exercises, the equation of a surface in rectangular coordinates is given. Find the equation of the surface in spherical coordinates. Identify the surface. \(\quad z=6\)

For the following exercises, the equation of a surface in rectangular coordinates is given. Find the equation of the surface in spherical coordinates. Identify the surface. \(x^{2}+y^{2}=9\)

For the following exercises, the cylindrical coordinates of a point are given. Find its associated spherical coordinates, with the measure of the angle \(\varphi\) in radians rounded to four decimal places. [T] \(\left(1, \frac{\pi}{4}, 3\right)\)

For the following exercises, the cylindrical coordinates of a point are given. Find its associated spherical coordinates, with the measure of the angle \(\varphi\) in radians rounded to four decimal places. [T] \((5, \pi, 12)\)

For the following exercises, the cylindrical coordinates of a point are given. Find its associated spherical coordinates, with the measure of the angle \(\varphi\) in radians rounded to four decimal places. \(\left(3, \frac{\pi}{2}, 3\right)\)

For the following exercises, the cylindrical coordinates of a point are given. Find its associated spherical coordinates, with the measure of the angle \(\varphi\) in radians rounded to four decimal places. \(\left(3,-\frac{\pi}{6}, 3\right)\)

For the following exercises, the spherical coordinates of a point are given. Find its associated cylindrical coordinates. \(\left(2,-\frac{\pi}{4}, \frac{\pi}{2}\right)\)

For the following exercises, the spherical coordinates of a point are given. Find its associated cylindrical coordinates. \(\left(4, \frac{\pi}{4}, \frac{\pi}{6}\right)\)