9. Polar Equations

In Exercises 33–40, polar coordinates of a point are given. Find the rectangular coordinates of each point. (7.4, 2.5)

Given the point in cylindrical coordinates $(-4,3,4)$, what are its spherical coordinates $(\rho ,\theta ,\phi )$?

Convert the point to rectangular coordinates.

$(0,\(\frac{7\pi}{4}\))$

Given the polar coordinates $(3,\frac{\pi }{4})$, what are the corresponding Cartesian coordinates?

In Exercises 41–48, the rectangular coordinates of a point are given. Find polar coordinates of each point. Express θ in radians. (−2, 2)

For each pair of polar coordinates, (c) give the rectangular coordinates for the point. See Examples 1 and 2(a).

(5 , ―60°)

What are the rectangular coordinates of the point whose polar coordinates are $(3,\frac{\pi }{6})$?

Convert the point to polar coordinates.

$(-1,-\(\sqrt{3}\))$

In Exercises 41–48, the rectangular coordinates of a point are given. Find polar coordinates of each point. Express θ in radians. _ (2,−2√3)

Convert the point to rectangular coordinates.

$(-3,0)$

Convert the point to rectangular coordinates.

$(-2,-\(\frac{\pi}{4}\))$

Convert the point to polar coordinates.

$(1,1)$

For each pair of polar coordinates, (c) give the rectangular coordinates for the point. See Examples 1 and 2(a).

(3 , 120°)

Convert the point to polar coordinates.

$(-2,2)$

Convert the point to rectangular coordinates.

$(4,\(\frac{\pi}{6}\))$