11.7
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Convert the point from cylindrical coordinates to rectangular coordinates.
(8, −π/4, 4)
(4
, 4
, 4)

How do you convert polar units to rectangle?
 x = rcos(theta)
 y = rsin(theta)
 z=z

Which octant is (2, pi/4, 3) in?
3

Which octant is (2, pi/6, 8) in?
7

Convert the point from rectangular coordinates to cylindrical coordinates.
(5, −5, 2)
(10/
, pi/4 , 2)

How do you change from rectangular units to polar?
 r^{2} = x^{2} + y^{2}
 tan() = y / x
 z = z

What is (2, pi/4, 3) in rectangular units?
(
, 
, 3)

What is (1 , 5pi/4 , 2) in rectangular units?
(
, 
, 2 )

What is (1 , 
, 4) in polar units?
(2, 4pi/3, 4)

Convert the point from rectangular coordinates to cylindrical coordinates.
(5
, −5, 8)
(10, pi/6, 8 )

Find an equation in cylindrical coordinates for the equation given in rectangular coordinates.
z = x^{2 }+ y^{2} − 6
z = r^{2} 6

Find an equation in cylindrical coordinates for the equation given in rectangular coordinates
x^{2} + y^{2} + z^{2} − 3z = 0
r^{2} + z^{2} − 3z = 0

^{}Find an equation in rectangular coordinates for the equation given in cylindrical coordinates.
r = 2
x^{2} + y^{2} = 4

Find an equation in rectangular coordinates for the equation given in cylindrical coordinates.
θ = π/3
x
 y = 0

Find an equation in rectangular coordinates for the equation given in cylindrical coordinates.
^{}r = 10 sin(θ)
x^{2} + (y5)^{2} = 25



Convert the point from rectangular coordinates to spherical coordinates.
(2, 0, 0)
(2,0,pi/2)

Convert the point from spherical coordinates to rectangular coordinates.
(10, π/6, π/4)

Convert the point from spherical coordinates to rectangular coordinates.
(8, π, π/2)
(8,0,0)

Find an equation in rectangular coordinates for the equation given in spherical coordinates.
ρ = 2
x^{2} + y^{2} + z^{2} = 4

Find an equation in rectangular coordinates for the equation given in spherical coordinates.
θ = π4
x  y = 0

Convert the point from cylindrical coordinates to spherical coordinates.
(7, π/3, 0)
(7, pi/3, pi/2)

Convert the point from spherical coordinates to cylindrical coordinates.
(20, π/3, π/3)
(
, pi/3, 10)

Convert the rectangular equation to an equation in cylindrical coordinates and spherical coordinates.
x^{2} + y^{2} + z^{2} = 36
 r^{2} + z^{2} =36
 = 6

Find an equation in rectangular coordinates for the equation given in spherical coordinates.
φ = π6
z^{2} = 3(x^{2} + y^{2})