General Knowledge
The conversion equivalents from cylindrical to rectangular. (r, θ, z) --> (?,?,?)
What is (r, θ, z) --> (x,y,z)?
Convert from rectangular to cylindrical:
(4sqrt(2), -4sqrt(2), 1)
What is (8, -pi/4, 1)?
Convert from cylindrical to rectangular
(-3, 0, -5)
What is (-3, 0, -5)?
Convert from rectangular to spherical:
(8, 0, 0)
What is (8, 0, pi/2)?
Conversion equations from cylindrical to rectangular containing the variables θ, x, y, and z.
What is
x=r cos θ
y=r sin θ
z=z
Convert from rectangular to cylindrical:
(6sqrt(3), -6, 6)
What is (12, -pi/6, 6)
Convert from cylindrical to rectangular: (4, -𝜋 /4, 3)
(2sqrt(2),-3sqrt(2),3)
Convert from rectangular to spherical:
(2sqrt(3), 6, -4)
What is (8, 𝜋/3, 2𝜋/3)?
Classes gone that Dr. Shim was gone from COVID.
What are 2 class periods?
Convert from spherical to cylindrical:
(17, 0, 𝜋)
What is (0, 0, -17)?
Convert from spherical to rectangular:
(5, 𝜋/4, 𝜋)
What is (0, 0, -5)?
Convert from cylindrical to spherical:
(1, 𝜋/2, 1)
What is (sqrt(2), 𝜋/2, 𝜋/4)
Cylindrical to spherical conversions.
What are
ρ = sqrt(r^2+z^2)
θ=θ
Φ = arccos (z/ρ)
Convert from spherical to cylindrical:
(2, -5𝜋/6, 𝜋/6)
What is (1, -5𝜋/6, sqrt(3)?
Convert from spherical to rectangular:
(8, 𝜋/6, 𝜋/4)
What is (2sqrt(6), 2sqrt(2), 4sqrt(2) ) ?
Convert from cylindrical to spherical:
(sqrt(6), 𝜋/4, sqrt(2))
What is (2sqrt(2), 𝜋/4, 𝜋/3)?
The simple spherical equation for a half cone.
What is ϕ=c?
Find an equation in cylindrical coordinates for the equation given in rectangular coordinates.
z=x^2+y^2-2
What is z=r^2-2?
Find an equation in rectangular coordinates for the equation given in cylindrical coordinates.
r = 14sin(𝜃)
What is x^2+(y-7)^2=49?
Find an equation in spherical coordinates for the equation given in rectangular coordinates.
x^2+y^2+z^2-2z=0
What is 𝜌 = 2 cos(φ)?